What do we mean by " The diagonal extraction procedure " in the extraction of sequence in the following proof taking from: http://leonard.perso.math.cnrs.fr/papers/Leonard-Orlicz%20spaces.pdf
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2026-02-23 07:14:09.1771830849
The diagonal extraction procedure?
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For each $k$, you have a subsequence $\{f_{k,n}^{\vphantom{k}}\}_n$ such that $f_{k,n}^{\vphantom{k}}\xrightarrow[n\to\infty]{} f$ pointwise $\mu_k$-a.e. More importantly, you can choose the subsequences in such a way that each is a subsequence of the previous one.
"Diagonal extraction procedure" means then to consider the sequence $\{f_{n,n}\}.$