TY - JOUR
T1 - Convergence of probability measures on separable banach spaces
AU - Grinblat, L.
PY - 1977/12
Y1 - 1977/12
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84966255471&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1977-0494377-6
DO - 10.1090/S0002-9939-1977-0494377-6
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AN - SCOPUS:84966255471
SN - 0002-9939
VL - 67
SP - 321
EP - 323
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -