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'''Theorem''' (Pettis, 1938)'''.''' A function ''f'' : ''X'' → ''B'' defined on a [[measure space]] (''X'', Σ, ''μ'') and taking values in a Banach space ''B'' is (strongly) measurable (with respect to Σ and the Borel ''σ''-algebra on ''B'') [[if and only if]] it is both weakly measurable and almost surely separably valued.
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