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|Type:||Artigo de periódico|
|Title:||Conditional Expectations And Martingales In Banach Function Spaces|
|Abstract:||A saturated Fatou function norm ¢ defined on the probability space (Ω, F,P) is called regular if for each sub-σ-field A of F the conditional expectation EA is a contractive linear operator from LQ into LQ. If QA denotes the restriction of Q to the A-measurable functions, it is proved that Q is regular if and only if Q′A=Q′ for each sub-σ-field A and if and only if Q has the levelling-length property. A regular norm Q is absolutely continuous if and only if each martingale of the form Enf, converges in LQ to f, and each martingale boundend in LQ is of the form Enf if and only if 1Ω is of absolutely continuous Q′ norm, where En denote conditional expectations with respect to a non-decreasing sequence of sub-σ-fields. An application to a problem of Peetre on the interpolation of some martingale spaces is also given. © 1983.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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