Theorems · Theorem · measure theory
MeasureTheory.Integrable.real_toNNReal
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
MeasureTheory.Integrable f μ → MeasureTheory.Integrable (fun x => ↑(f x).toNNReal) μ- Cited by
- 3 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.
Cites15
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
- absproof · cited by 1,814
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- NNReal.toRealstatement and proof · cited by 1,260
- lt_of_le_of_ltproof · cited by 432
- Real.toNNRealstatement and proof · cited by 267
- MeasureTheory.Integrable.aestronglyMeasurableproof · cited by 84
- Continuous.comp_aestronglyMeasurableproof · cited by 77
- MeasureTheory.lintegral_monoproof · cited by 51
- MeasureTheory.Integrable.hasFiniteIntegralproof · cited by 29
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_partproof · cited by 3
- MeasureTheory.exists_lt_lowerSemicontinuous_integral_ltproof · cited by 2
- MeasureTheory.eLpNorm_one_le_of_leproof · cited by 1