Theorems · Theorem · measure theory
IsFiniteMeasure.lintegral_lt_top_of_bounded_to_ennreal
∀ {α : Type u_1} [inst : MeasurableSpace α] (μ : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure μ]
{f : α → ENNReal}, (∃ c, ∀ (x : α), f x ≤ ↑c) → ∫⁻ (x : α), f x ∂μ < ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- NNRealstatement and proof · cited by 4,310
- Set.univproof · cited by 3,945
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.measure_ne_topproof · cited by 171
- MeasureTheory.Measure.restrict_univproof · cited by 76
- MeasureTheory.setLIntegral_lt_top_of_le_nnrealproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.lintegral_lt_top_of_nnrealproof · cited by 11
- MeasureTheory.exists_measurable_le_forall_setLIntegral_eqproof · cited by 1
- MeasureTheory.eLpNorm_lt_top_of_finiteproof · cited by 0