Probabilistic Metric Spaces

Nonfiction, Science & Nature, Mathematics, Applied
Cover of the book Probabilistic Metric Spaces by B. Schweizer, A. Sklar, Dover Publications
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Author: B. Schweizer, A. Sklar ISBN: 9780486143750
Publisher: Dover Publications Publication: October 14, 2011
Imprint: Dover Publications Language: English
Author: B. Schweizer, A. Sklar
ISBN: 9780486143750
Publisher: Dover Publications
Publication: October 14, 2011
Imprint: Dover Publications
Language: English
This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs.
The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
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This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs.
The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.

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