Strong Convergence and Weak Convergence

  • Kôsaku Yosida
Part of the Die 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.


Weak Convergence Strong Convergence Weak Topology Normed Linear Space Linear Topological Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Research Institute for Mathematical SciencesUniversity of KyotoKyotoJapan

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