Convergence of probability measures on separable banach spaces

L. Grinblat

doi:10.1090/S0002-9939-1977-0494377-6

Convergence of probability measures on separable banach spaces

L. Grinblat

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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

Original language	English
Pages (from-to)	321-323
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	67
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1977-0494377-6
State	Published - Dec 1977
Externally published	Yes

Access to Document

10.1090/S0002-9939-1977-0494377-6

Cite this

@article{01a26f97e4eb4e78a0057827954096ab,

title = "Convergence of probability measures on separable banach spaces",

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 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).",

author = "L. Grinblat",

year = "1977",

month = dec,

doi = "10.1090/S0002-9939-1977-0494377-6",

language = "אנגלית",

volume = "67",

pages = "321--323",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}

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 - https://www.scopus.com/pages/publications/84966255471

U2 - 10.1090/S0002-9939-1977-0494377-6

DO - 10.1090/S0002-9939-1977-0494377-6

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -

Convergence of probability measures on separable banach spaces

Abstract

Access to Document

Other files and links

Fingerprint

Cite this