Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_sum_of_countable
∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} [Countable ι] (μ : ι → MeasureTheory.Measure α) (s : Set α),
(MeasureTheory.Measure.sum μ).restrict s = MeasureTheory.Measure.sum fun i => (μ i).restrict s- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 2 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.
Cites14
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
- 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.extproof · cited by 308
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.Measure.sumstatement and proof · cited by 121
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.prod_restrictproof · cited by 12
- MeasureTheory.exists_measurable_le_forall_setLIntegral_eqproof · cited by 1