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Convex measure
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<p>In <a href="/facts/Measure_theory/yCq7zlI4">measure</a> and <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> in <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a convex measure is a <a href="/facts/Probability_measure/8BjhgoPR">probability measure</a> that — loosely put — does not assign more mass to any intermediate set "between" two <a href="/facts/Measurable_set/yCq7zlI4">measurable sets</a> <i>A</i> and <i>B</i> than it does to <i>A</i> or <i>B</i> individually. There are multiple ways in which the comparison between the probabilities of <i>A</i> and <i>B</i> and the intermediate set can be made, leading to multiple definitions of convexity, such as <a href="/facts/Logarithmically_concave_measure/v5KRoDsN">log-concavity</a>, harmonic convexity, and so on. The <a href="/facts/Mathematician/eaFSR8Fx">mathematician</a> Christer Borell was a pioneer of the detailed study of convex measures on <a href="/facts/Locally_convex_space/AGrPrayC">locally convex spaces</a> in the 1970s. </p>