A dichotomy for the convex spaces of probability measures |
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| Authors: | Miko?aj Krupski Grzegorz Plebanek |
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| Affiliation: | a Instytut Matematyczny, Polska Akademia Nauk, Ul. ?niadeckich 8, 00-956 Warszawa, Poland
b Instytut Matematyczny, Uniwersytet Wroc?awski, Pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland |
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| Abstract: | 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. |
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| Keywords: | primary, 46E27, 28C15 secondary, 46B26, 46E15 |
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