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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Israel Journal of Ma...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Israel Journal of Mathematics
Article . 1999 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Aronszajn null and Gaussian null sets coincide

Authors: Marianna Csörnyei;

Aronszajn null and Gaussian null sets coincide

Abstract

In the study of Gateaux differentiability of Lipschitz maps from separable Banach spaces into various types of spaces several authors have introduced notions of smallness for sets and have proved such functions are differentiable outside of an exceptional small set. The results of this type referenced in the present paper are: \textit{N. Aronszajn}, Stud. Math. 57, 147-190 (1976; Zbl 0342.46034); \textit{J. P. R. Christensen}, Publ. Dépt. Math., Lyon 10, No. 2, 29-39 (1973; Zbl 0302.43001); \textit{P. Mankiewicz}, Stud. Math. 45, 15-29 (1973; Zbl 0246.46002) and \textit{R. R. Phelps}, Pac. J. Math. 77, 523-531 (1978; Zbl 0396.46041)]. Three of these notions are: Aronszajn null sets; nondegenerate cube measure null sets; and Gaussian null sets. These are \(\sigma\)-ideals of sets \(\Sigma_1\), \(\Sigma_2\), and \(\Sigma_3\) respectively definable in any separable Banach space. It was previously known that \(\Sigma_1\subset (\Sigma_2 \cap \Sigma_3)\). The present author shows that \(\Sigma_1=\Sigma_2=\Sigma_3\).

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Keywords

Aronszajn null sets, Derivatives of functions in infinite-dimensional spaces, Gateaux differentiability, Lipschitz function, Gaussian null sets

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
26
Average
Top 10%
Top 10%
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