Theorems · Theorem · measure theory
MeasureTheory.Integrable.aemeasurable
∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
[inst_1 : ContinuousENorm ε] [inst_2 : MeasurableSpace ε] [BorelSpace ε] [TopologicalSpace.PseudoMetrizableSpace ε]
{f : α → ε}, MeasureTheory.Integrable f μ → AEMeasurable f μ- Cited by
- 10 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- AEMeasurablestatement · cited by 840
- ContinuousENormstatement and proof · cited by 290
- TopologicalSpace.PseudoMetrizableSpacestatement and proof · cited by 245
- MeasureTheory.Integrable.aestronglyMeasurableproof · cited by 84
- MeasureTheory.AEStronglyMeasurable.aemeasurableproof · cited by 73
Cited by10
Results whose statement or proof uses this declaration.
- ProbabilityTheory.aemeasurable_of_mem_interior_integrableExpSetproof · cited by 6
- ProbabilityTheory.aemeasurable_of_integrable_exp_mulproof · cited by 3
- MeasureTheory.mul_meas_ge_le_integral_of_nonnegproof · cited by 1
- MeasureTheory.condLExp_ofRealproof · cited by 1
- MeasureTheory.Integrable.integral_eq_integral_meas_ltproof · cited by 1
- volume_regionBetween_eq_integral'proof · cited by 1
- ProbabilityTheory.sum_prob_mem_Ioc_leproof · cited by 1
- MeasureTheory.integral_tendsto_of_tendsto_of_monotoneproof · cited by 1
- MeasureTheory.setIntegral_mono_of_nonnegproof · cited by 0
- ProbabilityTheory.IndepFun.integral_bilinproof · cited by 0