Titlebook: Differentiability of Six Operators on Nonsmooth Functions and p-Variation; Richard M. Dudley,Rimas Norvaiša Book 1999 Springer-Verlag Berl

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Quadrilingual Education in Singapore0. This is a question of continuity or equicontinuity of Nemytskii operators at points. Previously, for the most part, global continuity had been treated. The individual . are shown to be exactly those which are continuous almost everywhere, suitably measurable, and such that {.(.){/(1+{.{.) is boun

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Product integrals, young integrals and ,-variation,ity in the supremum norm, on sets uniformly bounded in 1-variation norm. The present paper shows that when restricted to rightor left-continuous elements of ., .is analytic. To prove these results a generalized Stieltjes integral due to L. C. Young is developed, as are variants of it called left You

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Differentiability of Six Operators on Nonsmooth Functions and p-Variation

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Product integrals, young integrals and ,-variation,. Then the product integral with respect to . over [.] is defined as the limit of the product from .=1 to . of .+.(..), if it exists, where the limit is taken under refinements of partitions. It is proved that the product integral with respect to . over [.] exists if .∈..([.];)., 0<.<2, i.e., if . h

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,Bibliographies on ,-variation and ϕ-variation,ion” as studied in probability theory and defined as a limit along a sequence of partitions {..} with mesh max.(....)→0, at some rate, or where the sums converge only in probability; (b) the special case .=1 of ordinary bounded variation; or (c) sequence spaces, called James spaces.