Theorems · Theorem · measure theory
MeasureTheory.IsZeroOneMeasure.measure_inter_eq_prod
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsZeroOneMeasure μ]
{s t : Set α}, MeasurableSet s → MeasurableSet t → μ (s ∩ t) = μ s * μ t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- mul_oneproof · cited by 3,885
- MeasurableSetstatement and proof · cited by 3,075
- MulZeroClass.mul_zeroproof · cited by 2,091
- Set.inter_subset_leftproof · cited by 360
- MeasureTheory.measure_monoproof · cited by 338
- Set.inter_subset_rightproof · cited by 329
- MeasureTheory.IsZeroOneMeasurestatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.isDeterministic_iff_isZeroOneMeasureproof · cited by 0