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A dichotomy for the convex spaces of probability measures

By Mikołaj Krupski and Grzegorz Plebanek


We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has `small' local character in M or else M contains a measure of `large' Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions.Comment: 10 page

Topics: Mathematics - Functional Analysis, 46E27, 28C15 (Primary) 46B26, 46E15 (Secondary)
Year: 2011
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