Existence
The set Tan(μ, a) of tangent measures of a measure μ at a point a in the support of μ is nonempty on mild conditions on μ. By the weak compactness of Radon measures, Tan(μ, a) is nonempty if one of the following conditions hold:
- μ is asymptotically doubling at a, i.e.
- μ has positive and finite upper density, i.e. for some .
Read more about this topic: Tangent Measure
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