Functions and Analysis

    

A Note on Lp-Convergence and Almost Everywhere Convergence

Authors: Yu-Lin Chou

It is a classical but relatively less well-known result that, for every given measure space and every given $1 \leq p \leq +\infty$, every sequence in $L^{p}$ that converges in $L^{p}$ has a subsequence converging almost everywhere. The typical proof is a byproduct of proving the completeness of $L^{p}$ spaces, and hence is not necessarily ``application-friendly''. We give a simple, perhaps more ``accessible'' proof of this result for all finite measure spaces.

Comments: 3 Pages. expository article

Download: PDF

Submission history

[v1] 2020-11-26 11:12:58

Unique-IP document downloads: 3772 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus