Theorems · Theorem · measure theory
MeasureTheory.hausdorffMeasure_segment
∀ {E : Type u_7} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E]
[inst_3 : BorelSpace E] (x y : E), (MeasureTheory.Measure.hausdorffMeasure 1) (segment ℝ x y) = edist x yThe measure of a segment is the distance between its endpoints.
- Defined in
- Mathlib.MeasureTheory.Measure.Hausdorff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- BorelSpacestatement and proof · cited by 1,602
- EDist.ediststatement and proof · cited by 735
- segmentstatement · cited by 120
- MeasureTheory.Measure.hausdorffMeasurestatement and proof · cited by 71
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