×

Martingales valued in certain subspaces of \(L^1\). (English) Zbl 0445.46015


MSC:

46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46B25 Classical Banach spaces in the general theory
46B20 Geometry and structure of normed linear spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
60G46 Martingales and classical analysis
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] J. Bourgain,Un espace non Radon-Nikodym sans arbre diadique, Seminaire d’Analyse Fonctionnelle 1978-79, Ecole Polytechnique, Palaiseau. · Zbl 0423.46010
[2] J. Bourgain,A non-dentable set without the RN property, Studia Math. (to appear).
[3] J. Bourgain and H. P. Rosenthal,Geometrical implications of certain finite dimensional decompositions, to appear. · Zbl 0463.46011
[4] Diestel, J.; Uhl, J. J., Vector Measures (1977), Providence: Amer. Math. Soc., Providence · Zbl 0369.46039
[5] Johnson, W. B.; Odell, E., Subspaces of L_p which embed into l_p, Comp. Math., 28, 37-49 (1974) · Zbl 0282.46020
[6] Lindenstrauss, J.; Tzafriri, L., Classical Banach Spaces (1973), Berlin, Heidelberg, New York: Springer-Verlag, Berlin, Heidelberg, New York · Zbl 0259.46011
[7] Loève, M., Probability Theory (1963), Princeton: D. van Nostrand Company, Princeton · Zbl 0108.14202
[8] N. T. Peck,An L_0-compact convex set in L_1with no extreme points, preliminary report.
[9] J. W. Roberts,Compact convex sets with no extreme points in the spacesL^p ([0, 1]), 0≦p<1, to appear.
[10] Rosenthal, H. P., A characterization of Banach spaces containing l^1, Proc. Nat. Acad. Sci. U.S.A., 71, 2411-2413 (1974) · Zbl 0297.46013 · doi:10.1073/pnas.71.6.2411
[11] H. P. Rosenthal,A subsequence splitting result for L^1-bounded sequences of random variables, in preparation.
[12] Stegall, C., The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc., 206, 213-223 (1975) · Zbl 0318.46056 · doi:10.2307/1997154
[13] Szarek, S. J., On the best constant in the Khintchine inequality, Studia Math., 63, 197-208 (1976) · Zbl 0424.42014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.