Abstract:Conditions for the absolute continuity of probability measures are given in terms of limits of sequences of Radon-Nikodym derivatives. In the other direction, conditions for the optional stopping theorem for positive martingales are given in terms of properties of their induced measures.
- Robert B. Ash, Real analysis and probability, Probability and Mathematical Statistics, No. 11, Academic Press, New York-London, 1972. MR 0435320 J. M. Kabanov, R. S. Lipcer and A. N. Shiryaev, On the question of absolute continuity and singularity of probability measures, Math. USSR Sb. 33, 203-221.
- J. Neveu, Discrete-parameter martingales, Revised edition, North-Holland Mathematical Library, Vol. 10, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. Translated from the French by T. P. Speed. MR 0402915
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 680-684
- MSC: Primary 60G30
- DOI: https://doi.org/10.1090/S0002-9939-1983-0718996-7
- MathSciNet review: 718996