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The -PIP and integrability of a single function

Authors:	Gunnar F Stefá nsson

Institution:	Department of Mathematics, Pennsylvania State University, Altoona Campus, Altoona, Pennsylvania 16601

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 in such that $x^{*}f=\lim_nfx_n$ a.e., does it follow that is Pettis integrable?

Keywords:	$\mathrm{weak}^*$ integral Pettis integral

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