Weakly measurable function: Difference between revisions

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'''Theorem''' (Pettis, 1938)'''.''' A function ''f''&nbsp;:&nbsp;''X''&nbsp;→&nbsp;''B'' defined on a [[measure space]] (''X'',&nbsp;Σ,&nbsp;''μ'') and taking values in a Banach space ''B'' is (strongly) measurable (withthat respectequals toa.e. Σthe andlimit theof Borela ''σ''-algebrasequence onof measurable countably-valued ''B''functions) [[if and only if]] it is both weakly measurable and almost surely separably valued.

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