Theorems · Theorem · measure theory
Real.Convex.dimH_eq_finrank_vectorSpan
∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {s : Set E},
Convex ℝ s → s.Nonempty → dimH s = ↑(Module.finrank ℝ ↥(vectorSpan ℝ s))The Hausdorff dimension of a nonempty convex set equals the dimension of its affine span.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- LE.le.transproof · cited by 3,151
- Set.Nonemptystatement and proof · cited by 2,627
- FiniteDimensionalstatement and proof · cited by 1,854
Cited by1
Results whose statement or proof uses this declaration.
- Real.dimH_segmentproof · cited by 0