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Counter-examples to
some conjectures about doubly stochastic measures
Viktor Losert |
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Vol. 99 (1982), No. 2, 387–397
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Abstract |
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Some new types of doubly stochastic measures are constructed. Using measure preserving transformations, one can construct examples of nontrivial extreme doubly stochastic measures which are absolutely continuous with respect to another extreme doubly stochastic measure (disproving a conjecture by Feldman). By combinatorial arguments, one gets an extreme doubly stochastic measure that is not concentrated on a countable union of function graphs and whose support is the whole unit square. |
Mathematical Subject Classification 2000
Primary: 28A35
Secondary: 60A10, 60J99
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Milestones
Received: 13 January 1981
Revised: 21 May 1981
Published: 1 April 1982
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Authors |
| Viktor Losert | |
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