Theorems · Theorem · measure theory
MeasureTheory.Integrable.mono_measure
∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
[inst_1 : ContinuousENorm ε] {f : α → ε}, MeasureTheory.Integrable f ν → μ ≤ ν → MeasureTheory.Integrable f μ- Cited by
- 26 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 1,367
- ContinuousENormstatement and proof · cited by 290
- MeasureTheory.Integrable.aestronglyMeasurableproof · cited by 84
- MeasureTheory.Integrable.hasFiniteIntegralproof · cited by 29
- MeasureTheory.AEStronglyMeasurable.mono_measureproof · cited by 13
- MeasureTheory.HasFiniteIntegral.mono_measureproof · cited by 3
Cited by26
Results whose statement or proof uses this declaration.
- MeasureTheory.IntegrableOn.monoproof · cited by 22
- MeasureTheory.Integrable.restrictproof · cited by 15
- MeasureTheory.IntegrableOn.unionproof · cited by 8
- MeasureTheory.integral_mono_measureproof · cited by 5
- MeasureTheory.VectorMeasure.IntegrableOn.monoproof · cited by 4
- MeasureTheory.hasSum_integral_measureproof · cited by 4
- MeasureTheory.Integrable.comp_add_rightproof · cited by 2
- MeasureTheory.IntegrableOn.mono_set_aeproof · cited by 2
- MeasureTheory.Integrable.comp_negproof · cited by 2
- MeasureTheory.setToFun_of_le_map_of_stronglyMeasurableproof · cited by 2
- MeasureTheory.integral_inter_add_sdiff₀proof · cited by 2
- MeasureTheory.Integrable.comp_add_leftproof · cited by 2