Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.restrict_apply_measure
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : MeasureTheory.FiniteMeasure Ω) (A : Set Ω) {s : Set Ω},
MeasurableSet s → ↑(μ.restrict A) s = ↑μ (s ∩ A)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.toMeasurestatement · cited by 87
- MeasureTheory.FiniteMeasure.restrictstatement · cited by 10
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