Real Analysis Exchange

On Some Modes of Convergence in Spaces with the Weak Banach-Saks Property

Marian Jakszto

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The paper proves a general theorem that relates some modes of convergence, such as pointwise a.e. convergence, to weak convergence in any space with the weak Banach-Saks property. Some results that follow immediately from the main theorem are given for specific functional spaces.

Article information

Real Anal. Exchange, Volume 38, Number 2 (2012), 487-492.

First available in Project Euclid: 27 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 46B20: Geometry and structure of normed linear spaces
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

weak Banach-Saks property weak convergence pointwise a.e. convergence convergence in measure


Jakszto, Marian. On Some Modes of Convergence in Spaces with the Weak Banach-Saks Property. Real Anal. Exchange 38 (2012), no. 2, 487--492.

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