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) = 1The Hausdorff dimension of a non-degenerate segment in a real normed space is 1.
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- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- Submoduleproof · cited by 7,192
- Nat.cast_oneproof · cited by 2,501
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- DivisionRingproof · cited by 1,062
- segmentstatement · cited by 120
- sub_ne_zeroproof · cited by 119
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