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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonstandard methods for families of $ \tau$-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 $ \tau $-smooth probability measures we give nonstandard characterizations of uniform $ \tau $-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: http://dx.doi.org/10.1090/S0002-9939-1988-0954998-8
PII: S 0002-9939(1988)0954998-8
Keywords: Uniformly $ \tau $-smooth, uniformly tight, weakly relatively compact families of $ p$-measures, Loeb-measures, theorem of Prohorov and Topsøe
Article copyright: © Copyright 1988 American Mathematical Society