Theorems · Theorem · measure theory
dimH_def
∀ {X : Type u_2} [inst : EMetricSpace X] [inst_1 : MeasurableSpace X] [inst_2 : BorelSpace X] (s : Set X),
dimH s = ⨆ d, ⨆ (_ : (MeasureTheory.Measure.hausdorffMeasure ↑d) s = ⊤), ↑dUnfold the definition of dimH using [MeasurableSpace X] [BorelSpace X] from the
environment.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- iSupstatement and proof · cited by 2,415
- BorelSpacestatement and proof · cited by 1,602
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- EMetricSpacestatement and proof · cited by 242
Cited by5
Results whose statement or proof uses this declaration.
- hausdorffMeasure_of_dimH_ltproof · cited by 5
- dimH_leproof · cited by 4
- le_dimH_of_hausdorffMeasure_eq_topproof · cited by 3
- hausdorffMeasure_of_lt_dimHproof · cited by 1
- dimH_eq_iInfproof · cited by 0