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 Mar16 comment Integration theory for Banach-valued functions Hi. Why is this integral unique by Hahn-Banach theorem? Feb24 comment Approximation of a strongly measurable function by a sequence of simple functions. @Freeze_S: Sorry, could not understand it. It is getting late for me. Good night and thank you very much. Feb24 comment Approximation of a strongly measurable function by a sequence of simple functions. @Freeze_S: But what I am asking about is how to prove (1) in the original proof. Feb24 comment Approximation of a strongly measurable function by a sequence of simple functions. @Freeze_S: How to make sure that $A_{n}(s_{k})$ is not empty? Feb24 comment Approximation of a strongly measurable function by a sequence of simple functions. Actually I don't have any idea about these supports, because we haven't studied any thing about them. I think that the statement in (1) can be proved via basic arguments using the density and the set of rational numbers. Feb24 revised Approximation of a strongly measurable function by a sequence of simple functions. added 2 characters in body Feb24 revised Approximation of a strongly measurable function by a sequence of simple functions. added 14 characters in body Feb24 revised Approximation of a strongly measurable function by a sequence of simple functions. added 161 characters in body Feb24 comment Approximation of a strongly measurable function by a sequence of simple functions. How to prove the statement labeled as (1) in the proof of the proposition in the image? Feb13 comment Approximation of a strongly measurable function by a sequence of simple functions. Sorry, I don't have such an account and you are welcome. Feb12 comment Approximation of a strongly measurable function by a sequence of simple functions. I think the answer is here Feb12 comment Approximation of a strongly measurable function by a sequence of simple functions. Measure Theory by Donald L. Cohn. page 351 Feb12 asked Approximation of a strongly measurable function by a sequence of simple functions. Feb1 comment A sufficient condition for the existence of a fixed point for a continuous function. Thank you very much. Feb1 accepted A sufficient condition for the existence of a fixed point for a continuous function. Feb1 asked A sufficient condition for the existence of a fixed point for a continuous function. Nov23 comment Singleton sets and net criteria for closeness I understood you now. Thank you very much. Nov23 comment Singleton sets and net criteria for closeness But the theorem, which I got from a book, implies that. Nov23 asked Singleton sets and net criteria for closeness Nov10 awarded Popular Question