Theorems · Theorem · measure theory
MeasureTheory.Integrable.congr
∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
[inst_1 : ContinuousENorm ε] {f g : α → ε}, MeasureTheory.Integrable f μ → f =ᵐ[μ] g → MeasureTheory.Integrable g μ- Cited by
- 28 results in Mathlib
- Foundations
- Depth 181 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.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- ContinuousENormstatement and proof · cited by 290
- MeasureTheory.AEStronglyMeasurable.congrproof · cited by 19
- MeasureTheory.HasFiniteIntegral.congrproof · cited by 3
Cited by28
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_congrproof · cited by 42
- MeasureTheory.integrable_condExpproof · cited by 28
- MeasureTheory.Martingale.integrableproof · cited by 10
- MeasureTheory.setToFun_congr_aeproof · cited by 10
- MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'proof · cited by 5
- MeasureTheory.IntegrableOn.congr_fun_aeproof · cited by 5
- MeasureTheory.IntegrableOn.of_ae_sdiff_eq_zeroproof · cited by 4
- MeasureTheory.setIntegral_eq_of_subset_of_ae_sdiff_eq_zeroproof · cited by 4
- MeasureTheory.WithDensityᵥEq.congr_aeproof · cited by 3
- MeasureTheory.SignedMeasure.eq_singularPartproof · cited by 3
- MeasureTheory.L1.SimpleFunc.setToL1S_nonnegproof · cited by 3
- integrableOn_mul_sum_Iccproof · cited by 3