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Martingale Convergence of Generalized Conditional Expectations

✍ Scribed by L. Accardi; R. Longo

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 394 KB
Volume: 118
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1993.1139

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that the martingale convergence theorem for generalized conditional expectations in von Neumann algebras holds in the weak topology without restrictions. The situation is therefore different fom the strong topology case, where there are restrictive conditions which distinguish between increasing and decreasing sequences of von Neumann algebras. Moreover, known couterexamples show that in the decreasing case the strong martingale convergence theorem might not hold.
C. 1993 Academic Press, Inc.

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