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On a measure-theoretic area formula

Part of: Classical measure theory

Published online by Cambridge University Press:  20 July 2015

Valentino Magnani
Valentino Magnani*
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy, ([email protected])
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Abstract

We review some classical differentiation theorems for measures, showing how they can be turned into an integral representation of a Borel measure with respect to a fixed Carathéodory measure. We focus our attention on the case when this measure is the spherical Hausdorff measure, giving a metric measure area formula. Our aim is to use certain covering derivatives as ‘generalized densities’. Some consequences for the sub-Riemannian Heisenberg group are also pointed out.

Keywords

differentiation of measuresHausdorff measurearea formulaa

MSC classification

Primary: 28A15: Abstract differentiation theory, differentiation of set functions
Secondary: 28A78: Hausdorff and packing measures
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 885 - 891
Copyright
Copyright © Royal Society of Edinburgh 2015 

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