Doubling subsets of Hilbert space admit pointwise and coarse tangent fields whose dimension is bounded by the Nagata or Assouad dimension of the set.
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A sufficient condition on a unital algebra of locally Lipschitz functions makes the energy-approximation BV space coincide with the standard metric BV space.
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Coarse and pointwise tangent fields
Doubling subsets of Hilbert space admit pointwise and coarse tangent fields whose dimension is bounded by the Nagata or Assouad dimension of the set.
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Functions of bounded variation and Lipschitz algebras in metric measure spaces
A sufficient condition on a unital algebra of locally Lipschitz functions makes the energy-approximation BV space coincide with the standard metric BV space.