Theorems · Theorem · measure theory
MeasureTheory.lintegral_ofReal_le_lintegral_enorm
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} (f : α → ℝ),
∫⁻ (x : α), ENNReal.ofReal (f x) ∂μ ≤ ∫⁻ (x : α), ‖f x‖ₑ ∂μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.ofRealstatement and proof · cited by 863
- ENorm.enormstatement · cited by 715
- le_abs_selfproof · cited by 113
- Real.norm_eq_absproof · cited by 88
- ENNReal.ofReal_le_ofRealproof · cited by 61
- MeasureTheory.lintegral_monoproof · cited by 51
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.lintegral_lt_topproof · cited by 5
- MeasureTheory.tendsto_of_integral_tendsto_of_monotoneproof · cited by 3