Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_iUnion_le
∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] {s : ι → Set α},
μ.restrict (⋃ i, s i) ≤ MeasureTheory.Measure.sum fun i => μ.restrict (s i)- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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.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
- MeasurableSetproof · cited by 3,075
- Set.iUnionstatement · cited by 2,483
- SummationFilter.unconditionalproof · cited by 2,068
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- tsumproof · cited by 1,148
- Countablestatement and proof · cited by 633
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.Measure.sumstatement · cited by 121
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_restrict_iUnion_eqproof · cited by 4
- MeasureTheory.aemeasurable_fderivWithinproof · cited by 2
- MeasureTheory.lintegral_iUnion_leproof · cited by 2
- MeasureTheory.AEStronglyMeasurable.iUnionproof · cited by 2
- AEMeasurable.iUnionproof · cited by 1