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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The $\mu$-PIP and integrability of a single function
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by Gunnar F. Stefánsson PDF
Proc. Amer. Math. Soc. 124 (1996), 539-542 Request permission

Abstract:

Two examples are given that answer in the negative the following question asked by E. M. Bator: If $f:\Omega \to X^*$ is bounded and weakly measurable and for each $x^{**}$ in $X^{**}$ there is a bounded sequence $(x_n)$ in $X$ such that $x^{**}f=\lim _nfx_n$ a.e., does it follow that $f$ is Pettis integrable?
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Additional Information
  • Gunnar F. Stefánsson
  • Affiliation: Department of Mathematics, Pennsylvania State University, Altoona Campus, Altoona, Pennsylvania 16601
  • Email: gfs@math.psu.edu
  • Received by editor(s): July 14, 1993
  • Received by editor(s) in revised form: September 7, 1994
  • Communicated by: Dale Alspach
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 539-542
  • MSC (1991): Primary 46G10, 28B05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03105-X
  • MathSciNet review: 1301529