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Reference.org
Weakly measurable function
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>—specifically, in <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a>—a weakly measurable function taking values in a <a href="/facts/Banach_space/sDEIk7EC">Banach space</a> is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> whose <a href="/facts/Function_composition/r5Pvnmth">composition</a> with any element of the <a href="/facts/Continuous_dual_space/4Uw4Knz1">dual space</a> is a <a href="/facts/Measurable_function/NgIHnb1b">measurable function</a> in the usual (strong) sense. For <a href="/facts/Separable_space/2bmU73bk">separable spaces</a>, the notions of weak and strong measurability agree. </p>