Theorems · Theorem · measure theory
MeasureTheory.integrable_zero
∀ (α : Type u_1) {m : MeasurableSpace α} (ε' : Type u_8) [inst : TopologicalSpace ε'] [inst_1 : ESeminormedAddMonoid ε']
(μ : MeasureTheory.Measure α), MeasureTheory.Integrable 0 μ- Cited by
- 22 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Integrablestatement · cited by 1,367
- ESeminormedAddMonoidstatement and proof · cited by 133
Cited by22
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_condExpproof · cited by 28
- MeasureTheory.integrable_finsetSum'proof · cited by 10
- MeasureTheory.condExp_zeroproof · cited by 9
- MeasureTheory.condExp_nonnegproof · cited by 7
- MeasureTheory.setToFun_zeroproof · cited by 6
- MeasureTheory.withDensityᵥ_zeroproof · cited by 5
- InformationTheory.klDiv_selfproof · cited by 4
- MeasureTheory.SimpleFunc.integrable_approxOn_rangeproof · cited by 4
- MeasureTheory.SignedMeasure.eq_singularPartproof · cited by 3
- MeasureTheory.integrableOn_zeroproof · cited by 3
- MeasureTheory.locallyIntegrable_zeroproof · cited by 2
- MeasureTheory.tendsto_integral_approxOn_of_measurable_of_range_subsetproof · cited by 2