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Strong Convergence and Weak Convergence

  • Kôsaku Yosida
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)

Abstract

In this chapter, we shall be concerned with certain basic facts pertaining to strong-, weak- and weak* convergences, including the comparison of the strong notion with the weak notion, e.g., strong- and weak measurability, and strong- and weak analyticity. We also discuss the integration of B-space-valued functions, that is, the theory of Bochner’s integrals. The general theory of weak topologies and duality in locally convex linear topological spaces will be given in the Appendix.

Keywords

Weak Convergence Strong Convergence Weak Topology Normed Linear Space Linear Topological Space 
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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References for Chapter V

  1. S. Banach [1], N. Dunford-J. Schwartz [1] and E. Hille-R. S. Phillips [1].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Kamakura, 247Japan

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