Wikipedia:WikiProject Mathematics/PlanetMath Exchange/28-XX Measure and integration

28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

 * PM: Comparison between Lebesgue and Riemann Integration, id=7343 -- WP: Lebesgue integration -- Status:


 * PM: bound on error of Simpson's rule, id=7979new! -- WP guess: bound on error of Simpson's rule -- Status:

28-01 Instructional exposition (textbooks, tutorial papers, etc.)

 * PM: an integrable function that does not tend to zero, id=9202new! -- WP guess: an integrable function that does not tend to zero -- Status:

28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets

 * PM: Borel \sigma-algebra, id=951 -- WP: Borel sigma-algebra -- Status: A
 * On PM they have just a lame definition. Oleg Alexandrov | talk 18:22, 5 Feb 2005 (UTC)


 * PM: limit superior of sets, id=3689 -- WP: limit superior of sets -- Status: A
 * Made it a redirect to limit superior and limit inferior where this info exists. Oleg Alexandrov (talk) 01:58, 24 October 2005 (UTC)


 * PM: measure zero, id=4898 -- WP guess: measure zero -- Status: A
 * On PM they just have a lame definition. Oleg Alexandrov | talk 21:19, 5 Feb 2005 (UTC)


 * PM: Kolmogorov zero-one law, id=9425new! -- WP guess: Kolmogorov zero-one law -- Status:


 * PM: monotone class, id=9426new! -- WP guess: monotone class -- Status:


 * PM: monotone class theorem, id=9429new! -- WP guess: monotone class theorem -- Status:


 * PM: proof of Vitali's Theorem, id=4467new! -- WP guess: proof of Vitali's Theorem -- Status:


 * PM: sequence of sets convergence, id=8358new! -- WP guess: sequence of sets convergence -- Status:


 * PM: sigma--ring of sets, id=9369new! -- WP guess: sigma--ring of sets -- Status:


 * PM: tail event, id=9424new! -- WP guess: tail event -- Status:

28A10 Real- or complex-valued set functions

 * PM: \sigma-finite, id=2723 -- WP: sigma-finite -- Status: A
 * Redirects to measure (mathematics) where this definition is stated. Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)


 * PM: Argand diagram, id=751 -- WP: Argand diagram -- Status: A
 * Redirects to complex number, where this info is covered.Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)


 * PM: Hahn-Kolmogorov theorem, id=5409 -- WP: Hahn-Kolmogorov theorem -- Status: C
 * Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)


 * PM: measure, id=756 -- WP: measure (mathematics) -- Status: A
 * Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)


 * PM: outer measure, id=4456 -- WP: outer measure -- Status: A
 * Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)


 * PM: properties for measure, id=4460 -- WP: measure (mathematics) -- Status: A
 * Oleg Alexandrov (talk) 08:51, 22 October 2005 (UTC)

28A12 Contents, measures, outer measures, capacities

 * PM: absolutely continuous, id=3997 -- WP guess: absolutely continuous -- Status:


 * PM: complete measure, id=5520 -- WP: complete measure -- Status: A
 * Oleg Alexandrov (talk) 02:03, 24 October 2005 (UTC)


 * PM: completion of a measure space, id=5521 -- WP: completion of a measure space -- Status: A
 * Redirects to measure (mathematics) where this concept is explained. Oleg Alexandrov (talk) 07:18, 24 October 2005 (UTC)


 * PM: counting measure, id=2096 -- WP: counting measure -- Status: A
 * Oleg Alexandrov (talk) 07:18, 24 October 2005 (UTC)


 * PM: Hahn decomposition theorem, id=4014 -- WP: Hahn decomposition theorem -- Status: M
 * Merged and redirected to signed measure. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)


 * PM: Jordan decomposition, id=4015 -- WP: signed measure -- Status: M
 * Merged to signed measure. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)


 * PM: Lebesgue decomposition theorem, id=4003 -- WP: Lebesgue's decomposition theorem -- Status: C
 * Oleg Alexandrov (talk) 19:48, 8 March 2006 (UTC)


 * PM: Lebesgue outer measure, id=341 -- WP: Outer measure -- Status: A
 * We have the fully general defintion in any measure space, not just the real line. Oleg Alexandrov (talk) 19:51, 8 March 2006 (UTC)


 * PM: outer regular, id=2938 -- WP: outer regular -- Status: A
 * linas 16:19, 26 August 2006 (UTC)


 * PM: proof that the outer (Lebesgue) measure of an interval is its length, id=6435 -- WP guess: proof that the outer (Lebesgue) measure of an interval is its length -- Status:


 * PM: signed measure, id=4013 -- WP: signed measure -- Status: C
 * Copied and merged with Hahn decomposition theorem and Jordan decomposition. Oleg Alexandrov (talk) 08:49, 24 October 2005 (UTC)


 * PM: singular measure, id=4002 -- WP: singular measure -- Status: C
 * Oleg Alexandrov (talk) 19:48, 8 March 2006 (UTC)


 * PM: support of integrable function with respect to counting measure is countable, id=6698 -- WP guess: support of integrable function with respect to counting measure is countable -- Status:


 * PM: Bolyai-Gerwien theorem, id=8720new! -- WP guess: Bolyai-Gerwien theorem -- Status:


 * PM: continuous almost everywhere versus equal to a continuous function almost everywhere, id=7996new! -- WP guess: continuous almost everywhere versus equal to a continuous function almost everywhere -- Status:


 * PM: quasi-invariant, id=7942new! -- WP guess: quasi-invariant -- Status:

28A15 Abstract differentiation theory, differentiation of set functions

 * PM: Hardy-Littlewood maximal operator, id=4024 -- WP guess: Hardy-Littlewood maximal operator -- Status:


 * PM: Hardy-Littlewood maximal theorem, id=4025 -- WP guess: Hardy-Littlewood maximal theorem -- Status:


 * PM: integral depending on a parameter, id=4517 -- WP guess: integral depending on a parameter -- Status:


 * PM: Lebesgue differentiation theorem, id=4026 -- WP guess: Lebesgue differentiation theorem -- Status:


 * PM: Radon-Nikodym theorem, id=3998 -- WP: Radon-Nikodym theorem -- Status: M
 * Oleg Alexandrov (talk) 04:58, 27 October 2005 (UTC)

28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

 * PM: dominated convergence theorem, id=3677 -- WP: dominated convergence theorem -- Status: A
 * Oleg Alexandrov (talk) 03:51, 25 October 2005 (UTC)


 * PM: Egorov's theorem, id=3699 -- WP: Egorov's theorem -- Status: A
 * Oleg Alexandrov (talk) 03:51, 25 October 2005 (UTC)


 * PM: Fatou's lemma, id=3678 -- WP: Fatou's lemma -- Status: A
 * Oleg Alexandrov (talk) 03:52, 25 October 2005 (UTC)


 * PM: Fatou-Lebesgue theorem, id=3679 -- WP guess: Fatou-Lebesgue theorem -- Status:


 * PM: measurable function, id=3176 -- WP: measurable function -- Status: A
 * Oleg Alexandrov (talk) 05:02, 27 October 2005 (UTC)


 * PM: proof of dominated convergence theorem, id=4077 -- WP guess: proof of dominated convergence theorem -- Status:


 * PM: proof of dominated convergence theorem, id=6123 -- WP guess: proof of dominated convergence theorem -- Status:


 * PM: proof of Egorov's theorem, id=4518 -- WP guess: proof of Egorov's theorem -- Status:


 * PM: proof of Fatou's lemma, id=4076 -- WP guess: proof of Fatou's lemma -- Status:


 * PM: uniformly integrable, id=7211 -- WP guess: uniformly integrable -- Status:


 * PM: almost continuous function, id=8329new! -- WP guess: almost continuous function -- Status:


 * PM: criterion for interchanging summation and integration, id=8465new! -- WP guess: criterion for interchanging summation and integration -- Status:


 * PM: Lusin's theorem, id=8330new! -- WP guess: Lusin's theorem -- Status:


 * PM: modes of convergence of sequences of measurable functions, id=8335new! -- WP guess: modes of convergence of sequences of measurable functions -- Status:


 * PM: proof of Fatou-Lebesgue theorem, id=7997new! -- WP guess: proof of Fatou-Lebesgue theorem -- Status:


 * PM: regarding the sets A_n from the traveling hump sequence, id=8344new! -- WP guess: regarding the sets A_n from the traveling hump sequence -- Status:


 * PM: traveling hump sequence, id=8336new! -- WP guess: traveling hump sequence -- Status:


 * PM: Vitali convergence theorem, id=8401new! -- WP guess: Vitali convergence theorem -- Status:

28A25 Integration with respect to measures and other set functions

 * PM: L^{\infty}(X, d\mu), id=4797 -- WP guess: L^\infty(X, d\mu) -- Status:


 * PM: \mathbb{L}^p vs \mathbb{L}^q, id=7194 -- WP guess: \mathbbL^p vs \mathbbL^q -- Status:


 * PM: Clarkson inequality, id=8142new! -- WP guess: Clarkson inequality -- Status:


 * PM: proof of Clarkson inequality, id=8562new! -- WP guess: proof of Clarkson inequality -- Status:

28A33 Spaces of measures, convergence of measures

 * PM: Koch curve, id=1186 -- WP: Koch curve -- Status: A
 * linas 16:24, 26 August 2006 (UTC)


 * PM: measurable space, id=755 -- WP: measurable space -- Status: A
 * linas 16:35, 26 August 2006 (UTC)


 * PM: weak-* topology of the space of Radon measures, id=7212 -- WP guess: weak-* topology of the space of Radon measures -- Status:

28A35 Measures and integrals in product spaces

 * PM: Fubini's theorem for the Lebesgue integral, id=5719 -- WP guess: Fubini's theorem for the Lebesgue integral -- Status:


 * PM: product measure, id=952 -- WP: product measure -- Status: C
 * Oleg Alexandrov (talk) 13:01, 24 October 2005 (UTC)


 * PM: Tonelli's theorem, id=5713 -- WP: Tonelli's theorem -- Status: A
 * Oleg Alexandrov (talk) 13:01, 24 October 2005 (UTC)


 * PM: proof of Fubini's theorem for the Lebesgue integral, id=7189 -- WP guess: proof of Fubini's theorem for the Lebesgue integral -- Status:


 * PM: infinite product measure, id=8532new! -- WP guess: infinite product measure -- Status:

28A60 Measures on Boolean rings, measure algebras

 * PM: \sigma-algebra, id=950 -- WP guess: sigma-algebra -- Status: A
 * Oleg Alexandrov (talk) 14:14, 24 October 2005 (UTC)


 * PM: \sigma-algebra, id=4835 -- WP: sigma-algebra -- Status: A
 * PM has two articles on this topic for some reason. Oleg Alexandrov (talk) 14:14, 24 October 2005 (UTC)


 * PM: algebra, id=1918 -- WP: algebra -- Status:


 * PM: measurable set (for outer measure), id=4458 -- WP guess: measurable set (for outer measure) -- Status:

28A75 Length, area, volume, other geometric measure theory

 * PM: example 1 of integration with respect to surface area, id=6664 -- WP guess: example 1 of integration with respect to surface area -- Status:


 * PM: example 2 of integration with respect to surface area, id=6665 -- WP guess: example 2 of integration with respect to surface area -- Status:


 * PM: example 3 of integration with respect to surface area, id=6666 -- WP guess: example 3 of integration with respect to surface area -- Status:


 * PM: example 4 of integration with respect to surface area, id=6667 -- WP guess: example 4 of integration with respect to surface area -- Status:


 * PM: example 5 of integration with respect to surface area, id=6668 -- WP guess: example 5 of integration with respect to surface area -- Status:


 * PM: example 6 of integration with respect to surface area, id=6669 -- WP guess: example 6 of integration with respect to surface area -- Status:


 * PM: example 7 of integration with respect to surface area, id=6672 -- WP guess: example 7 of integration with respect to surface area -- Status:


 * PM: example 8 of integration with respect to surface area, id=6673 -- WP guess: example 8 of integration with respect to surface area -- Status:


 * PM: integration with respect to surface area, id=6660 -- WP guess: integration with respect to surface area -- Status:


 * PM: Lebesgue density theorem, id=3869 -- WP: Lebesgue density theorem -- Status: C
 * Oleg Alexandrov (talk) 04:26, 3 March 2006 (UTC)


 * PM: derivation of first formula for surface integration with respect to area, id=6862 -- WP guess: derivation of first formula for surface integration with respect to area -- Status:


 * PM: derivation of second formula for surface integration with respect to area, id=6863 -- WP guess: derivation of second formula for surface integration with respect to area -- Status:


 * PM: invariance of formula for surface integration with respect to area under change of variables, id=6865 -- WP guess: invariance of formula for surface integration with respect to area under change of variables -- Status:

28A78 Hausdorff and packing measures

 * PM: area formula, id=5979 -- WP guess: area formula -- Status:


 * PM: Hausdorff measure, id=5976 -- WP guess: Hausdorff measure -- Status:

28A80 Fractals

 * PM: Cantor set, id=2083 -- WP: Cantor set -- Status: NM
 * PM discussion of fat Cantor sets needs to be merged or put to fat Cantor set. linas 16:27, 26 August 2006 (UTC)


 * PM: fractal, id=2979 -- WP guess: fractal -- Status: A
 * Jeekc 14:56, 8 January 2006 (UTC)


 * PM: Hausdorff dimension, id=2981 -- WP guess: Hausdorff dimension -- Status:


 * PM: Menger sponge, id=5968 -- WP: Menger sponge -- Status: A
 * linas 16:29, 26 August 2006 (UTC)


 * PM: Sierpinski gasket, id=3011 -- WP: Sierpinski gasket -- Status: A
 * linas 16:30, 26 August 2006 (UTC)


 * PM: Barnsley fern, id=8154new! -- WP guess: Barnsley fern -- Status:


 * PM: closure and interior of Cantor set, id=7671new! -- WP guess: closure and interior of Cantor set -- Status:


 * PM: Douady rabbit, id=9602new! -- WP guess: Douady rabbit -- Status:


 * PM: Julia set, id=9593new! -- WP guess: Julia set -- Status:


 * PM: Mandelbrot set, id=9237new! -- WP guess: Mandelbrot set -- Status:


 * PM: Peano curve, id=8723new! -- WP guess: Peano curve -- Status:


 * PM: proof of existence and unicity of self-similar fractals, id=8153new! -- WP guess: proof of existence and unicity of self-similar fractals -- Status:


 * PM: quadratic Julia set, id=9574new! -- WP guess: quadratic Julia set -- Status:


 * PM: San Marco dragon, id=9603new! -- WP guess: San Marco dragon -- Status:


 * PM: self-similar fractals, id=8146new! -- WP guess: self-similar fractals -- Status:

28B05 Vector-valued set functions, measures and integrals

 * PM: vector measure, id=9877new! -- WP guess: vector measure -- Status:

28B15 Set functions, measures and integrals with values in ordered spaces

 * PM: L^p-space, id=2047 -- WP guess: L^p-space -- Status:


 * PM: locally integrable function, id=4430 -- WP: locally integrable function -- Status: C
 * Oleg Alexandrov (talk) 04:51, 3 March 2006 (UTC)


 * PM: fundamental lemma of calculus of variations, id=6745 -- WP: fundamental lemma of calculus of variations -- Status: M
 * Copied the references. Oleg Alexandrov (talk) 20:00, 8 March 2006 (UTC)


 * PM: example of function not Lebesgue Measurable with measurable level sets, id=7841new! -- WP guess: example of function not Lebesgue Measurable with measurable level sets -- Status:

28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections

 * PM: Fractional calculus, id=8430new! -- WP guess: Fractional calculus -- Status:

28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures

 * PM: Haar integral, id=4324 -- WP guess: Haar integral -- Status:


 * PM: Radon measure, id=7797new! -- WP guess: Radon measure -- Status:

28C10 Set functions and measures on topological groups, Haar measures, invariant measures

 * PM: Haar measure, id=2959 -- WP: Haar measure -- Status: A
 * Oleg Alexandrov (talk) 05:32, 25 October 2005 (UTC)

28C15 Set functions and measures on topological spaces (regularity of measures, etc.)

 * PM: Krylov-Bogolubov theorem, id=5525 -- WP guess: Krylov-Bogolubov theorem -- Status:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

 * PM: essential supremum, id=2044 -- WP: essential supremum -- Status: C
 * Oleg Alexandrov (talk) 04:27, 3 March 2006 (UTC)

28D05 Measure-preserving transformations

 * PM: measure-preserving, id=1950 -- WP: measure-preserving -- Status: A
 * linas 16:32, 26 August 2006 (UTC)

28D20 Entropy and other invariants

 * PM: entropy of a partition, id=6076 -- WP guess: entropy of a partition -- Status:


 * PM: metric entropy, id=6077 -- WP guess: metric entropy -- Status:

28E99 Miscellaneous

 * PM: proof of pseudoparadox in measure theory, id=6233 -- WP guess: proof of pseudoparadox in measure theory -- Status:


 * PM: proof that a finite collection of sets will not suffice, id=6234 -- WP guess: proof that a finite collection of sets will not suffice -- Status:


 * PM: pseudoparadox in measure theory, id=6232 -- WP guess: pseudoparadox in measure theory -- Status: