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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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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

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