Strong Convergence and Weak Convergence

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


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.


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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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