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The $\mu$-PIP and integrability of a single function

Author: Gunnar F. Stefánsson
Journal: Proc. Amer. Math. Soc. 124 (1996), 539-542
MSC (1991): Primary 46G10, 28B05
MathSciNet review: 1301529
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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

Keywords: $\mathrm {weak}^*$ integral, Pettis integral
Received by editor(s): July 14, 1993
Received by editor(s) in revised form: September 7, 1994
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society