Theorems · Theorem · measure theory
MeasureTheory.HasFiniteIntegral.of_bounded
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
[MeasureTheory.IsFiniteMeasure μ] {f : α → β} {C : ℝ},
(∀ᵐ (a : α) ∂μ, ‖f a‖ ≤ C) → MeasureTheory.HasFiniteIntegral f μ- Cited by
- 8 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.HasFiniteIntegralstatement · cited by 120
- MeasureTheory.HasFiniteIntegral.mono'proof · cited by 8
- MeasureTheory.hasFiniteIntegral_constproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.of_boundproof · cited by 6
- MeasureTheory.HasFiniteIntegral.of_finiteproof · cited by 3
- MeasureTheory.HasFiniteIntegral.restrict_of_boundedproof · cited by 3
- ContinuousOn.integrableOn_of_subset_isCompactproof · cited by 3
- MeasureTheory.integral_integral_swap_of_hasCompactSupportproof · cited by 2
- MeasureTheory.AEContinuous.hasBoxIntegralproof · cited by 1
- MeasureTheory.integrable_resolventproof · cited by 1
- MeasureTheory.StronglyAdapted.integrable_upcrossingsBeforeproof · cited by 1