Abstract
This note gives another proof of the known fact that \(L^{p}\)-bounded pointwise convergence implies weak convergence in \(L^{p},\) \(p>1.\) The proof is based on Banach and Saks’ theorem. The same method applies to convergence in measure.
Citation
Marian Jakszto. "Another Proof That Lp-Bounded Pointwise Convergence Implies Weak Convergence." Real Anal. Exchange 36 (2) 479 - 482, 2010/2011.
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