Some open mapping theorems for marginals
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- by Larry Q. Eifler PDF
- Trans. Amer. Math. Soc. 211 (1975), 311-319 Request permission
Abstract:
Let S and T be compact Hausdorff spaces and let $P(S),P(T)$ and $P(S \times T)$ denote the collection of probability measures on S, T and $S \times T$, respectively. Given a probability measure $\mu$ on $S \times T$, set $\pi \mu = (\alpha ,\beta )$ where $\alpha$ and $\beta$ are the marginals of $\mu$ on S and T. We prove that the mapping $\pi :P(S \times T) \to P(S) \times P(T)$ is norm open and ${\text {weak}^\ast }$ open. An analogous result for ${L_1}(X \times Y,\mu \times \nu )$ where $(X,\mu )$ and $(Y,\nu )$ are probability spaces is established.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 211 (1975), 311-319
- MSC: Primary 28A35; Secondary 60B05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0387533-1
- MathSciNet review: 0387533