Talk:Caccioppoli set

A proposal for the plan of the voice
I have decided to detail my proposal by using a few numbered steps. I hope this voice will attract the interest of readers and other contributors/criticizers alike. :) Daniele.tampieri 20:30, 13 February 2007 (UTC)
 * 1) Well, first of all there must be a short Informal definition which gives at least the feel of what a Caccioppoli set is.
 * 2) Closely following it would be interesting to trace a little the History of the concept, the names of the original contributors to its development, dates and stuff like that.
 * 3) Next starts the hard part of the subject: the Formal definition, giving the reader a rigorous, respect to present (2007) standards, definition of the concept.
 * 4) Things come getting harder, so the Properties section begins, listing (hopefully all) important properties of the concept and sketching related proofs (or not, depending on their lenght).
 * 5) Now a bit of relax, starting with the See also section, giving the reader a quich overview of related Wiki voices.
 * 6) Then follows the list of References used by the editor for the ones who want to probe further.
 * 7) A (hopefully rich) landscape of topics not even touched is shown by the Bibliography section.
 * 8) At last, an overview of what the internet has to offer, adequately although briefly described, is presented in the External links sections.

Major overhaul
I have taken the liberty to significantly rewrite the second half of the article and add some extra stuff. It is important to account for reduced boundaries and De Giorgi's theorem, which are arguably the whole point behind sets of locally finite perimeter.

That said, I am concerned that maybe the article is too dense or too technical now, in which case I'd appreciate someone else giving it a facelift. I don't know if it's a good idea to split this up into two-three articles as it is (they would be small), but that would be fine too. December 2013.

Slight Mistake
The second point of the Properties section seems to be wrong. Equality does not imply $$d(E_1,E_2)>0$$. Sets may touch in a point and the perimeter is invariant under nullset pertubations. Also consider proper subsets. In the last term there is an $$\Omega_1$$ that is unnecessary. I also think that the more powerful statement is that for all measurable sets $$E_1,E_2$$ we have $$P(E_1 \cup E_2,\Omega) + P(E_1 \cap E_2,\Omega) \leq P(E_1,\Omega) + P(E_2, \Omega)$$. 129.217.64.141 (talk) 15:52, 13 June 2023 (UTC)