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2005•Chinese Annals of Mathematics,series ARequires access

GEOMETRIC ANALYSIS OF TANGENT MEASURES

Vang Xiaoping

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Abstract

The authors study the tangent measures of a Radon measure μ and obtain the rectifia-bility of tangent measures and the existence of the micro tangent set of a continuous function by using the duality and the blow-up technique. The authors also give out the properties of flatness of tangent measures. As an application of tangent measures, the authors, with the help of Energy of μ, prove further the Marstrand's theorem.

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What this paper is about

The authors study the tangent measures of a Radon measure μ and obtain the rectifia-bility of tangent measures and the existence of the micro tangent set of a continuous function by using the duality and the blow-up technique. The authors also give out the properties of flatness of tangent measures. As an application of tangent measures, the authors, with the help of Energy of μ, prove further the Marstrand's theorem.

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Available abstract

The authors study the tangent measures of a Radon measure μ and obtain the rectifia-bility of tangent measures and the existence of the micro tangent set of a continuous function by using the duality and the blow-up technique. The authors also give out the properties of flatness of tangent measures. As an application of tangent measures, the authors, with the help of Energy of μ, prove further the Marstrand's theorem.

Key concepts: Tangent cone, Tangent, Tangent vector, Flatness (cosmology), Mathematics, Duality (order theory), Measure (data warehouse), Function (biology)

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