Pointwise in terms of weak convergence

J. R. Baxter

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Let (Ω,?, p) be a measure space, µ(Ω) ∞. Let X be a sequence of measurable functions on Ω taking values in a compact metric space M. The set of bounded shopping times r for the X isa directed set under the obvious ordering. The following theorem is proved: X converges pointwise almost everywhere if and only if the generalized n sequence 4Ø(Xt)du converges for every continuous function Ø on M. The martingale theorem is proved as an application.

Original languageEnglish (US)
Pages (from-to)395-398
Number of pages4
JournalProceedings of the American Mathematical Society
Volume46
Issue number3
DOIs
StatePublished - Dec 1974

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