Convergence of probability measures on separable Banach spaces

Author:
L. Š. Grinblat

Journal:
Proc. Amer. Math. Soc. **67** (1977), 321-323

MSC:
Primary 60B10

MathSciNet review:
0494377

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Abstract: The following result follows immediately from a general theorem on the convergence of probability measures on separable Banach spaces: On the space there exists a norm equivalent to the ordinary norm such that if and are continuous random processes and for any finite set of points the joint distribution of converges to the joint distribution of then converges weakly to .

**[1]**V. D. Milman,*Geometric theory of Banach spaces. II. Geometry of the unit ball*, Uspehi Mat. Nauk**26**(1971), no. 6(162), 73–149 (Russian). MR**0420226****[2]**L. Š. Grinblat,*Compactifications of spaces of functions and integration of functionals*, Trans. Amer. Math. Soc.**217**(1976), 195–223. MR**0407227**, 10.1090/S0002-9947-1976-0407227-4**[3]**L. Š. Grinblat,*Convergence of random processes without discontinuities of the second kind and limit theorems for sums of independent random variables*, Trans. Amer. Math. Soc.**234**(1977), no. 2, 361–379. MR**0494376**, 10.1090/S0002-9947-1977-0494376-9**[4]**L. Š. Grinblat,*A limit theorem for measurable random processes and its applications*, Proc. Amer. Math. Soc.**61**(1976), no. 2, 371–376 (1977). MR**0423450**, 10.1090/S0002-9939-1976-0423450-2

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DOI:
https://doi.org/10.1090/S0002-9939-1977-0494377-6

Article copyright:
© Copyright 1977
American Mathematical Society