Theorems · Theorem · measure theory
MeasureTheory.Integrable.pos_part
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
MeasureTheory.Integrable f μ → MeasureTheory.Integrable (fun a => max (f a) 0) μ- Cited by
- 5 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.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.Integrable.aestronglyMeasurableproof · cited by 84
- MeasureTheory.aestronglyMeasurable_constproof · cited by 44
- MeasureTheory.Integrable.hasFiniteIntegralproof · cited by 29
- MeasureTheory.AEStronglyMeasurable.fun_supproof · cited by 1
- MeasureTheory.HasFiniteIntegral.max_zeroproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.neg_partproof · cited by 3
- MeasureTheory.integral_le_measureproof · cited by 2
- ProbabilityTheory.strong_law_ae_realproof · cited by 2
- MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_subproof · cited by 1
- MeasureTheory.integral_abs_eq_two_mul_integral_posPart_sub_integralproof · cited by 0