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MR2823095 (2012g:28012) 28B05 (28A10 46G10 60A10)
Dai, Peng; Feinberg, Eugene A. On maximal ranges of vector measures for subsets and purification of transition probabilities. Proc. Amer. Math. Soc. 139 (2011), no. 12, 4497–4511.
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