{"product_id":"9781783264704","title":"Probabilistic Normed Spaces","description":"\u003cp\u003eThis 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.\u003c\/p\u003e  \u003cp\u003eThe 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:\u003c\/p\u003e   \u003cul\u003e   \u003cli\u003eWhat are PN spaces?\u003c\/li\u003e   \u003cli\u003eThe topology of PN spaces\u003c\/li\u003e   \u003cli\u003eProbabilistic norms and convergence\u003c\/li\u003e   \u003cli\u003eProducts and quotients of PN spaces\u003c\/li\u003e   \u003cli\u003e\n\u003ci\u003eD\u003c\/i\u003e-boundedness and \u003ci\u003eD\u003c\/i\u003e-compactness\u003c\/li\u003e   \u003cli\u003eNormability\u003c\/li\u003e   \u003cli\u003eInvariant and semi-invariant PN spaces\u003c\/li\u003e   \u003cli\u003eLinear operators\u003c\/li\u003e   \u003cli\u003eStability of some functional equations in PN spaces\u003c\/li\u003e   \u003cli\u003eMenger's 2-probabilistic normed spaces\u003c\/li\u003e  \u003c\/ul\u003e   \u003cp\u003eThe 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.\u003c\/p\u003e\u003cstrong\u003eContents:\u003c\/strong\u003e  \u003cul\u003e   \u003cli\u003ePreliminaries\u003c\/li\u003e   \u003cli\u003eProbabilistic Normed Spaces\u003c\/li\u003e   \u003cli\u003eThe Topology of PN Spaces\u003c\/li\u003e   \u003cli\u003eProbabilistic Norms and Convergence\u003c\/li\u003e   \u003cli\u003eProducts and Quotients of PN Spaces\u003c\/li\u003e   \u003cli\u003e\n\u003ci\u003eD\u003c\/i\u003e-Boundedness and \u003ci\u003eD\u003c\/i\u003e-Compactness\u003c\/li\u003e   \u003cli\u003eNormability\u003c\/li\u003e   \u003cli\u003eInvariant and Semi-Invariant PN Spaces\u003c\/li\u003e   \u003cli\u003eLinear Operators\u003c\/li\u003e   \u003cli\u003eStability of Some Functional Equations in PN Spaces\u003c\/li\u003e   \u003cli\u003eMenger's 2-Probabilistic Normed Spaces\u003c\/li\u003e  \u003c\/ul\u003e  \u003cbr\u003e  \u003cstrong\u003eReadership:\u003c\/strong\u003e Post graduate students and researchers in the field of Probabilistic Normed Spaces.  \u003cb\u003eKey Features:\u003c\/b\u003e  \u003cul\u003e \u003cli\u003eThe 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\u003c\/li\u003e \u003cli\u003eDeals with all the developed ideas in PN spaces\u003c\/li\u003e \u003cli\u003eA good reference book for post graduate students and researchers in this field as it identifies the developments and open problems in PN spaces\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Imperial College Press","offers":[{"title":"Default Title","offer_id":47140047716592,"sku":"9781783264704","price":35.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781783264704_p0.jpg?v=1763723151","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781783264704","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}