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Theorems · Theorem · measure theory

Real.dimH_segment

∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {x y : E},
  x ≠ y → dimH (segment ℝ x y) = 1

The Hausdorff dimension of a non-degenerate segment in a real normed space is 1.

Defined in
Mathlib.Topology.MetricSpace.HausdorffDimension
Cited by
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Foundations
Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceFiniteDimensional

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