Banach-Saks Theorem for L1 Revisited
DOI:
https://doi.org/10.65135/atsf.2026.15Keywords:
Banach-Saks property, weak convergence, L^p-spacesAbstract
The Banach-Saks property is an important tool in analysis with applications ranging from partial differential equations (PDEs) to calculus of variations and probability theory. We survey the Banach-Saks property for Lp-spaces, with a particular emphasis on the case p=1. In other words, we revisit the celebrated result by W. Szlenk (1965) in a more general context, demonstrating that L1-spaces possess the weak Banach-Saks property.
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