Properties
The collection of tangent measures at a point is closed under two types of scaling. Cones of measures were also defined by Preiss.
- The set Tan(μ, a) of tangent measures of a measure μ at a point a in the support of μ is a cone of measures, i.e. if and, then .
- The cone Tan(μ, a) of tangent measures of a measure μ at a point a in the support of μ is a d-cone or dilation invariant, i.e. if and, then .
At typical points in the support of a measure, the cone of tangent measures is also closed under translations.
- At μ almost every a in the support of μ, the cone Tan(μ, a) of tangent measures of μ at a is translation invariant, i.e. if and x is in the support of ν, then .
Read more about this topic: Tangent Measure
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