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This article is cited in 1 scientific paper (total in 1 paper)
The existence of probability measures with specified projections
V. N. Sudakov Leningrad branch of V. A. Steklov Mathematical Institute of USSR Academy of Sciences
Abstract:
Let $X$ and $Y$ be locally compact $\sigma$-compact topological spaces, $F\subset X\times Y$ is closed, and $P(F)$ is the set of all Borel probability measures on $F$. For us to find, for the pair of probability measures $(\mu_X,\mu_Y)\in P(X)\times P(Y)$, a probability measure $\mu\in P(F)$ such that $\mu_X=\mu\pi_X^{-1}$, $\mu_Y=\mu\pi_Y{-1}$ it is necessary and sufficient that, for any pair of Borel sets $A\in X$, $B\subset Y$ for which $(A\times B)\cap F=\emptyset$, the condition $\mu_XA+\mu_YB\le1$ holds.
Received: 18.10.1971
Citation:
V. N. Sudakov, “The existence of probability measures with specified projections”, Mat. Zametki, 14:4 (1973), 573–576; Math. Notes, 14:4 (1973), 886–888
Linking options:
https://www.mathnet.ru/eng/mzm7291 https://www.mathnet.ru/eng/mzm/v14/i4/p573
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Abstract page: | 216 | Full-text PDF : | 80 | First page: | 1 |
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