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area formulaa

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

On a measure-theoretic area formula
Part of
- Classical measure theory
Valentino Magnani
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 4 / August 2015

Published online by Cambridge University Press:

20 July 2015, pp. 885-891

Print publication:

August 2015
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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.