Theorems · Theorem · measure theory
MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
∫⁻ (x : α), f x ∂μ ≠ ⊤ → MeasureTheory.HasFiniteIntegral (fun x => (f x).toReal) 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- ENNReal.ofNNRealproof · cited by 1,279
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.ofRealproof · cited by 863
- ENNReal.toRealstatement and proof · cited by 859
- ENorm.enormproof · cited by 715
- lt_of_le_of_ltproof · cited by 432
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.integrable_rnDerivproof · cited by 9
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2
- MeasureTheory.mem_L1_toReal_of_lintegral_ne_topproof · cited by 1