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
• DOI: 10.1007/bf00367303

✦ 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.