Talk:Final value theorem

My original dicussion was incorrect, I've such deleted my discussion. — Preceding unsigned comment added by 99.224.81.146 (talk) 02:23, 17 December 2011 (UTC)

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 * Added tag to http://wikis.controltheorypro.com/index.php?title=Final_Value_Theorem
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Proof using dominated convergence theorem
Regarding this version of page, I believe that the proof using dominated convergence theorem is incomplete. The only assumptions in the statement of final value theorem is that $$f$$ is bounded on $$(0,\infty)$$ and that $$\lim_{t \rightarrow \infty} f(t)$$ is finite. To use the dominated convergence theorem, however, we also require that $$f$$ is dominated by an integrable function.

This example shows that DCT does not hold for a sequence of only-bounded functions: https://math.stackexchange.com/questions/506571/characteristic-function-and-dominated-convergence-theorem Saung Tadashi (talk) 15:15, 20 August 2018 (UTC)


 * Tried to solve this issue by rewriting the proof. If you are an experienced Wikipedia editor or Mathematician, please review it. Gratefully, Saung Tadashi (talk) 00:48, 24 August 2018 (UTC)


 * Perhaps the Proof using the dominated convergence theorem bit ought to be removed? The article on Math Stack Exchange https://math.stackexchange.com/questions/3218574/a-proof-for-the-final-value-theorem-using-dominated-convergence-theorem discusses why the proof does not appear to work.  Spectrum629 (talk) 04:22, 22 April 2020 (UTC)


 * I agree in removing it. The change of variables part needs more rigorous justification and the proof by Pantelis Sopasakis on Math Stack Exchange is more elegant. Saung Tadashi (talk) 02:28, 23 April 2020 (UTC)