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TANGENT MEASURES OF TYPICAL MEASURES

机译:典型措施的切线措施

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摘要

We prove that for a typical Radon measure μ in R~d, every non-zero Radon measure is a tangent measure of μ at μ, almost every point. This was already shown by T. O'Neil in his Ph.D. thesis from 1994, but we provide a different self-contained proof for this fact. Moreover, we show that this result is sharp: for any non-zero measure we construct a point in its support where the set of tangent measures does not contain all nonzero measures. We also study a concept similar to tangent measures on trees, micromeasures, and show an analogous typical property for them.
机译:我们证明,对于R〜d中的典型Radon度量μ,几乎每个点上的每个非零Radon度量都是μ处的μ的切线度量。这已经由奥尼尔(T. O'Neil)在其博士学位中证明。论文来自1994年,但我们为此提供了另一种独立的证据。此外,我们证明了这一结果是很明显的:对于任何非零度量,我们在其支持点上构造了一个切线度量集不包含所有非零度量的点。我们还研究了类似于树木的切线量度,微观量度的概念,并显示了类似的典型特性。

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