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On the sequential approximation of scalarly measurable functions by simple functions. (English) Zbl 0539.46035

In this paper, the author studied the sequential approximation of weak*- measurable functions by means of simple functions. By using the martingale argument, he obtained some results which guarantee the existence of such sequential approximation. The most important one of them is that every norm-bounded Pettis integrable function has the sequential approximation, if the base measure space is perfect, which also has been proved by R. Geits [Proc. Am. Math. Soc. 82, 81-86 (1981; Zbl 0506.28007)] in a different way. He also showed that WCG Banach spaces (especially, separable Banach spaces) and Banach spaces not containing \(\ell_ 1\) have duals with the sequential approximation property.
Reviewer: M.Matsuda

MSC:

46G10 Vector-valued measures and integration
28B05 Vector-valued set functions, measures and integrals
60G46 Martingales and classical analysis

Citations:

Zbl 0506.28007
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