Theorems · Theorem · measure theory
MeasureTheory.measure_toMeasurable
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} (s : Set α),
μ (MeasureTheory.toMeasurable μ s) = μ s- Cited by
- 53 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.univproof · cited by 3,945
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aeproof · cited by 2,352
- Filter.EventuallyEqproof · cited by 1,912
- Set.inter_univproof · cited by 198
- MeasurableSet.univproof · cited by 178
- MeasureTheory.toMeasurablestatement · cited by 77
Cited by53
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.prod_prodproof · cited by 38
- MeasurableEmbedding.map_applyproof · cited by 16
- IsCompact.measure_closureproof · cited by 10
- Set.exists_isOpen_lt_of_ltproof · cited by 7
- MeasureTheory.Measure.restrict_eq_selfproof · cited by 6
- ProbabilityTheory.Kernel.exists_ae_eq_isMarkovKernelproof · cited by 6
- aeSeq.measure_compl_aeSeqSet_eq_zeroproof · cited by 5
- MeasureTheory.Measure.le_map_applyproof · cited by 5
- MeasureTheory.MemLp.mono_exponent_of_measure_support_ne_topproof · cited by 4
- AEMeasurable.exists_ae_eq_range_subsetproof · cited by 4