Nonstandard methods for families of smooth probability measures
Authors:
Dieter Landers and Lothar Rogge
Journal:
Proc. Amer. Math. Soc. 103 (1988), 11511156
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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 Patrick Billingsley, Convergence of probability measures, Wiley, New York, 1968. MR 0233396 (38:1718)
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 Peter A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113122. MR 0390154 (52:10980)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809549988
PII:
S 00029939(1988)09549988
Keywords:
Uniformly smooth,
uniformly tight,
weakly relatively compact families of measures,
Loebmeasures,
theorem of Prohorov and Topsøe
Article copyright:
© Copyright 1988
American Mathematical Society
