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This book provides a comprehensive foundation in Probabilistic
Normed (PN) Spaces for anyone conducting research in this field of
mathematics and statistics. It is the first to fully discuss the
developments and the open problems of this highly relevant topic,
introduced by A N Serstnev in the early 1960s as a response to
problems of best approximations in statistics.The theory was
revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who
provided a new, wider definition of a PN space which quickly became
the standard adopted by all researchers. This book is the first
wholly up-to-date and thorough investigation of the properties,
uses and applications of PN spaces, based on the standard
definition. Topics covered include:The theory of PN spaces is
relevant as a generalization of deterministic results of linear
normed spaces and also in the study of random operator equations.
This introduction will therefore have broad relevance across
mathematical and statistical research, especially those working in
probabilistic functional analysis and probabilistic geometry.
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