Convergence of probability measures on separable banach spaces

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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 ξ1(t),… ξn(t),…and ξ(t) are continuous random processes (0 ≤ t ≤ 1) and for any finite set of points t1,…, tk ⊂ [0, 1] the joint distribution of p(ξn), ξn(t1),…, ξn(tk) converges to the joint distribution of p(ξ), ξ(t1),…, ξ(tk) then ξn(t) converges weakly to ξ(t).

Original languageEnglish
Pages (from-to)321-323
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Dec 1977
Externally publishedYes


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