Real Analysis Exchange

Absolutely Continuous Functions with Values in a Metric Space

Jakub Duda

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Abstract

We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallée Poussin theorems.

Article information

Source
Real Anal. Exchange, Volume 32, Number 2 (2006), 569-582.

Dates
First available in Project Euclid: 3 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1199377494

Mathematical Reviews number (MathSciNet)
MR2369866

Zentralblatt MATH identifier
1131.26006

Subjects
Primary: 26A46: Absolutely continuous functions
Secondary: 26E20: Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]

Keywords
Absolutely continuous function with values in a metric space metric differentials Banach-Zarecki Theorem Vallée Poussin Theorem

Citation

Duda, Jakub. Absolutely Continuous Functions with Values in a Metric Space. Real Anal. Exchange 32 (2006), no. 2, 569--582. https://projecteuclid.org/euclid.rae/1199377494


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