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On measure derivation in metric spaces

Part of: Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  26 February 2010

Pio Andrea Zanzotto
Pio Andrea Zanzotto
Affiliation:
Dipartimento di Matematica dell' Universita, v. Buonarroti 2, 56100 Pisa, Italy.
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Abstract

We consider a metric space (X, ρ) of a certain class studied by H. Federer in “Geometric Measure Theory”. Let Ф be any derivation basis on X, which is formed by open balls and is ρ-fine. We show that Ф allows mutual derivation of two arbitrary Borel regular measures on X, which are σ-finite and finite-valued on bounded sets. The proof is based on the so-called De Giorgi property studied in a previous paper.

MSC classification

Secondary: 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)
Type
Research Article
Information
Mathematika , Volume 36 , Issue 2 , December 1989 , pp. 349 - 358
Copyright
Copyright © University College London 1989

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