Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces

Niko Marola; William P. Ziemer

doi:10.2969/jmsj/06720561

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces

Niko Marola, William P. Ziemer

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Keywords: area formula, condition N, doubling measure, Luzin's condition, metric space, Newtonian space, Poincaré inequality, Sobolev space, upper gradient

JOURNAL FREE ACCESS

2015 Volume 67 Issue 2 Pages 561-579

DOI https://doi.org/10.2969/jmsj/06720561

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Abstract

We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincaré inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.

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