# Questions tagged [lebesgue-integral]

For questions about integration, where the theory is based on measures. It is almost always used together with the tag [measure-theory], and its aim is to specify questions about integrals, not only properties of the measure.

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### Integral Criteria for Functions to be Zero Almost Everywhere

While reading the proof of Lemma 2 in the following link, I realized they only proved the case of a nonnegative function $f$, but that's not an hypothesis of the lemma. So, what happens if $f$ takes ...
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### A question in functional equation of Gamma Function

I have a question in Tom M Apostol ( Mathematical Analysis) Example on Page 278. I beg for every one's pardon, by mistake a different image was added. I am really sorry for wastage of other people's ...
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### Deducing Lebesgue Integration from Riemann Integrability of a function [duplicate]

I have a question which I thought while studying a theorem in Chaptee Lebesgue Integration from Tom Apostol and it may seem easy but can anyone please tell about it. Question: Assume that a function ...
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### Asking for help in proof of part of a Theorem in Apostol Mathematiccal Analysis ( A part which is not proved)

While self studying Lebesgue Integration from Apostol Mathematical Analysis I am struck on this theorem Image-> I am not able to understand how if theorem is true for {$s_n$ - $s_1$} then it's ...
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### Asking for proof verification of a theorem in Apostol Mathematical Analysis

I am self studying Apostol Mathematical Analysis Ch-> Lebesgue integration and I have a different thinking about a proof whose only outline is given in Apostol Book. It's image is -> In part (a)...