Theorems · Theorem · measure theory
MeasureTheory.measurableSet_toMeasurable
∀ {α : Type u_1} [inst : MeasurableSpace α] (μ : MeasureTheory.Measure α) (s : Set α),
MeasurableSet (MeasureTheory.toMeasurable μ s)- Cited by
- 62 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aeproof · cited by 2,352
- Filter.EventuallyEqproof · cited by 1,912
- MeasureTheory.toMeasurablestatement · cited by 77
- MeasureTheory.exists_measurable_supersetproof · cited by 10
- MeasureTheory.toMeasurable_defproof · cited by 6
Cited by62
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
- MeasureTheory.NullMeasurableSet.exists_measurable_subset_ae_eqproof · cited by 9
- MeasureTheory.withDensity_apply'proof · cited by 9
- Set.exists_isOpen_lt_of_ltproof · cited by 7
- MeasureTheory.Measure.restrict_apply₀'proof · cited by 7
- MeasureTheory.Measure.restrict_eq_selfproof · cited by 6
- ProbabilityTheory.Kernel.exists_ae_eq_isMarkovKernelproof · cited by 6
- Directed.measure_iUnionproof · cited by 5
- MeasureTheory.Measure.le_map_applyproof · cited by 5
- MeasureTheory.MemLp.mono_exponent_of_measure_support_ne_topproof · cited by 4