Related Concepts
There is an associated notion of the tangent space of a measure. A k-dimensional subspace P of Rn is called the k-dimensional tangent space of μ at a ∈ Ω if — after appropriate rescaling — μ “looks like” k-dimensional Hausdorff measure Hk on P. More precisely:
- Definition. P is the k-dimensional tangent space of μ at a if there is a θ > 0 such that
- where μa,r is the translated and rescaled measure given by
- The number θ is called the multiplicity of μ at a, and the tangent space of μ at a is denoted Ta(μ).
Further study of tangent measures and tangent spaces leads to the notion of a varifold.
Read more about this topic: Tangent Measure
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