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L1-Sequential Convergence on Stone Spaces and Stone's Theorem on Unitary Semigroups

Published online by Cambridge University Press:  20 November 2018

J. B. Cooper
J. B. Cooper*
Affiliation:
Mathematisches InstitutHochschule, Llnz A4045, Linz, Austria
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The following theorem is a well-known tool in the study of measurable functions:

Theorem. Let (M; μ) be a finite measure space and let (xn) be a sequence of functions in L1(M; μ) so that xn→0 in the norm of L1(M; μ). Then there is a sub-sequence so that xnk →0 pointwise almost everywhere on M.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 191 - 193
Copyright
Copyright © Canadian Mathematical Society 1975