On the span of some three valued martingale difference sequences in \(L^ p\) \((1<p<\infty)\) and \(H^ 1\)
type: Item
instance of: scholarly article
title: On the span of some three valued martingale difference sequences in \(L^ p\) \((1<p<\infty)\) and \(H^ 1\)
zbMATH Open document ID: 0656.46011
DOI: 10.1007/BF02766169
author: Paul F. X. Müller
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A sequence \(\{u_ n\}\) of measurable functions on a probability space is called a martingale difference sequence (m.d.s.) if for every n the conditional expectation of \(u_ n\) with respect to the algebra, generated by \(\{u_ 1,...,u_{n-1}\}\), is equal to zero. A m.d.s. \(\{u_ n\}\) is called nested if supp \(u_ i\cap \sup p u_ j\neq \emptyset\) implies that either supp \(u_ i\subset \sup p u_ j\) or supp \(u_ j\subset \sup p u_ i\). Let \(X^ p\) denote the span of a nested \(\{\)-1,0,1\(\}\)-valued m.d.s. in \(L^ p.\) The main result of the paper: the spaces \(L^ p\), \(\ell^ p\), \(\ell^ 2\), \(\ell^ p\oplus \ell^ 2\), \((\sum \oplus \ell^ 2)_ p\) are the only isomorphic types of \(X^ p\).
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 60G46
zbMATH DE Number: 4071645
zbMATH Keywords: martingale difference sequence
zbMATH Keywords: conditional expectation
zbMATH Keywords: nested
zbMATH Keywords: isomorphic types
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4071645