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Topological Vector Spaces

  • Bernard R. Gelbaum
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Because E≠(f, 0) is σ-finite, E= lim n→∞ for some sets E n of finite measure. Hence
$$ \int {_X f(x)d\mu (x) = \int {_E f(x)} d\mu (x) = _{n \to \infty }^{\lim } \int {_{E_n } } f(x)d\mu (x) \leqslant a} $$
.

Keywords

Banach Space Pairwise Disjoint Topological Vector Space Approximate Identity Monotone Convergence Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Bernard R. Gelbaum
    • 1
  1. 1.Department of MathematicsState University of New York (SUNY)BuffaloUSA

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