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Potential Analysis

, Volume 6, Issue 1, pp 87–97 | Cite as

A Note on Capacity and Hausdorff Measure in Homogeneous Spaces

  • Tord Sjödin
Article

Abstract

ggt We consider analogoues of classical Riesz capacity Cα and Hausdorff measure Hα in a homogeneous space (X,d,µ) . We prove that, under mild regularity conditions on (X,d,µ), the usual relations between Cα and Hα hold. The key step in the proof is a version of the so called Frostman Lemma in a homogeneous space.

Homogeneous space doubling measure Hausdorff measure Hausdorff dimension Riesz potential capacity Frostman lemma 

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© Kluwer Academic Publishers 1997

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  • Tord Sjödin

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