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 incre
โฆ LIBER โฆ
Joint convergence of conditional expectations
โ Scribed by Dieter Landers; Lothar Rogge
- Publisher
- Springer
- Year
- 1972
- Tongue
- English
- Weight
- 192 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0025-2611
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A necessary and sufficient condition on a sequence n nโN of ฯ-subalgebras that assures L p -convergence of the conditional expectations is given. This result generalizes the L p -martingales, the Fetter and the Boylan (equiconvergence) theorems.