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Synopsis
Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.
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Probability in Banach spaces, 8 : proceedings of the eighth international conference / Richard M. Dudley . (Ed.); Progress in probability ; Vol. 30
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Boston ; Basel ; Berlin : Birkhäuser,, 1992
ISBN 10: 3764336579
ISBN 13: 9783764336578
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Hardcover
Seller: Licus Media, Utting a. Ammersee, Germany
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Gebundene Ausgabe. Condition: Gut. en, Literaturangaben. XI, 510 S. ; 24 cm In English language. Illustrated hardbound (no dust jacket). Former library copy with external labelings removed from boards. Spine slightly discoloured, otherwise in very good condition. Signature stamps and inscriptions on endpapers and title. + + + Original-Pappeinband (kein Schutzumschlag). Ordentlich ausgesondertes Bibliotheksexemplar mit entfernten äußerlichen Kennzeichnungen. Einbandrücken geringf. aufgehellt, sonst textsauber und gepflegt. Signatur- / Entwidmungsstempel a. Vorsatz u. Titel. 3764336579 Werktäglicher Versand. Jede Lieferung m. ordentl. Rechnung und ausgew. MwSt. Der Versand erfolgt als Büchersendung / Einschreiben mit der Deutschen Post bzw. als Päckchen / Paket mit DHL. Die Lieferzeit ist abhängig von der Versandart und beträgt innerhalb Deutschlands 3-5 Tage, in der EU 5 - 12 Tage. KEIN Versand an Packstationen. Körperschaften und juristische Personen werden auf Wunsch per offener Rechnung beliefert. Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 47372
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