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arXiv · 1801.09572

A new Cartan-type property and strict quasicoverings when $p=1$ in metric spaces

Panu Lahti
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Abstract

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of $1$-finely open \emph{strict subsets} and \emph{strict quasicoverings} of $1$-finely open sets. As an application, we study fine Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined on $1$-finely open sets.

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Panu Lahti. 2018-01-26. A new Cartan-type property and strict quasicoverings when $p=1$ in metric spaces. https://arxiv.org/abs/1801.09572

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