Convergence of probability measures on separable Banach spaces
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- by L. Š. Grinblat PDF
- Proc. Amer. Math. Soc. 67 (1977), 321-323 Request permission
Abstract:
The following result follows immediately from a general theorem on the convergence of probability measures on separable Banach spaces: On the space $C[0,1]$ there exists a norm $p(x)$ equivalent to the ordinary norm such that if ${\xi _1}(t), \ldots ,{\xi _n}(t), \ldots$ and $\xi (t)$ are continuous random processes $(0 \leqslant t \leqslant 1)$ and for any finite set of points ${t_1}, \ldots ,{t_k} \subset [0,1]$ the joint distribution of $p({\xi _n}),{\xi _n}({t_1}), \ldots ,{\xi _n}({t_k})$ converges to the joint distribution of $p(\xi ),\xi ({t_1}), \ldots ,\xi ({t_k})$ then ${\xi _n}(t)$ converges weakly to $\xi (t)$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 321-323
- MSC: Primary 60B10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0494377-6
- MathSciNet review: 0494377