Nonstandard methods for families of -smooth probability measures

Authors:
Dieter Landers and Lothar Rogge

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1151-1156

MSC:
Primary 28E05; Secondary 28A33, 60B10

MathSciNet review:
954998

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Abstract: For families of -smooth probability measures we give nonstandard characterizations of uniform -smoothness, uniform tightness, uniform pretightness, and relative compactness in the weak topology. We apply these characterizations to obtain two important theorems of probability theory: A theorem of Topsøe and a theorem of Prohorov.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0954998-8

Keywords:
Uniformly -smooth,
uniformly tight,
weakly relatively compact families of -measures,
Loeb-measures,
theorem of Prohorov and Topsøe

Article copyright:
© Copyright 1988
American Mathematical Society