Theorems · Theorem · measure theory
MeasureTheory.lintegral_mono
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} ⦃f g : α → ENNReal⦄,
f ≤ g → ∫⁻ (a : α), f a ∂μ ≤ ∫⁻ (a : α), g a ∂μ- Cited by
- 51 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- le_reflproof · cited by 2,061
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.lintegral_mono'proof · cited by 12
Cited by51
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_add_leftproof · cited by 21
- MeasureTheory.exists_measurable_le_lintegral_eqproof · cited by 8
- MeasureTheory.iSup_lintegral_measurable_le_eq_lintegralproof · cited by 4
- MeasureTheory.monotone_lintegralproof · cited by 4
- MeasureTheory.HasFiniteIntegral.smulproof · cited by 4
- MeasureTheory.lintegral_liminf_le'proof · cited by 3
- MeasureTheory.lintegral_map_leproof · cited by 3
- MeasureTheory.Integrable.real_toNNRealproof · cited by 3
- MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_topproof · cited by 3
- MeasureTheory.lintegral_le_measproof · cited by 2
- MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimateproof · cited by 2
- MeasureTheory.lintegral_ofReal_le_lintegral_enormproof · cited by 2