Displaying similar documents to “Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces”

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)

Analysis and Geometry in Metric Spaces

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We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

Thin and fat sets for doubling measures in metric spaces

Tuomo Ojala, Tapio Rajala, Ville Suomala (2012)

Studia Mathematica

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We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.

A note on the Poincaré inequality

Alireza Ranjbar-Motlagh (2003)

Studia Mathematica

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The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

Poincaré Inequalities for Mutually Singular Measures

Andrea Schioppa (2015)

Analysis and Geometry in Metric Spaces

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Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.

A non-doubling Trudinger inequality

Amiran Gogatishvili, Pekka Koskela (2005)

Studia Mathematica

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We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.