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Almost surely convergent random variables with given laws

✍ Scribed by Andreas Schief


Publisher
Springer
Year
1989
Tongue
English
Weight
351 KB
Volume
81
Category
Article
ISSN
1432-2064

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✦ Synopsis


Let/Z, --*/Z be a weakly converging sequence of Borel probability measures on a topological space X. We prove the existence of an almost surely converging sequence of random variables 4, ~ r which obey this laws, if a certain/z-dependent countability property of the topology holds. Especially this is the case if (a) X is second countable, (b) X is first countable and # has countable support, (c) X is metrizable and/Z is v-smooth. A final example disproves the existence of such random variables for (tight) measures on a Lusin space.


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