Geometry and Martingales in Banach Spaces

"The author provides detailed proofs of all the results concerning the interplay between the geometry and martingales. For purely geometric or probabilistic results only references are given, the prerequisites being familiarity with basic facts of functional analysis and probability theory. The book is of interest for researchers in Banach spaces, probability theory and their applications to the analysis of vector functions."

-Stefan Cobzas, Babes-Bolyai University, Department of Mathematics, Romania

"In the 1970s there was frenetic activity in the field of probability in Banach spaces, propelled by mathematicians like, to name but a few, A. Araujo, P. Assouad, E. Gine, J. Hoffmann-Jorgensen, G. Pisier, L. Schwartz, N.N. Vakhaniya, J. Zinn and of course the present author,W. Woyczynski. The monograph under review sums up many of the results obtained in thisdecade, highlighting the interplay between probabilistic ideas and properties of Banach spaces,specifcally the Radon-Nikodym property (RNP) and local properties; indeed, the local theory of Banach spaces emerged as a result of these activities."

-Dirk Werner, Freie Universität Berlin, Berlin

"The author provides detailed proofs of all the results concerning the interplay between the geometry and martingales. For purely geometric or probabilistic results only references are given, the prerequisites being familiarity with basic facts of functional analysis and probability theory. The book is of interest for researchers in Banach spaces, probability theory and their applications to the analysis of vector functions."

-Stefan Cobzas,Babes-Bolyai University, Department of Mathematics, Romania

"In the 1970s there was frenetic activity in the field of probability in Banach spaces, propelled by mathematicians like, to name but a few, A. Araujo, P. Assouad, E. Gine, J. Hoffmann-Jorgensen, G. Pisier, L. Schwartz, N.N. Vakhaniya, J. Zinn and of course the present author,W. Woyczynski. The monograph under review sums up many of the results obtained in thisdecade, highlighting the interplay between probabilistic ideas and properties of Banach spaces,specifcally the Radon-Nikodym property (RNP) and local properties; indeed, the local theory of Banach spaces emerged as a result of these activities."

-Dirk Werner, Freie Universität Berlin, Berlin