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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)[reply]

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Proof using dominated convergence theorem

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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 is bounded on and that is finite. To use the dominated convergence theorem, however, we also require that 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)[reply]

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)[reply]
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)[reply]
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)[reply]