Theorems · Theorem · measure theory
MeasureTheory.lintegral_norm_eq_lintegral_edist
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
(f : α → β), ∫⁻ (a : α), ENNReal.ofReal ‖f a‖ ∂μ = ∫⁻ (a : α), edist (f a) 0 ∂μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Norm.normstatement · cited by 5,413
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.ofRealstatement · cited by 863
- EDist.ediststatement · cited by 735
- ENorm.enormproof · cited by 715
- ofReal_normproof · cited by 39
- edist_zero_rightproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.norm_toL1_eq_lintegral_normproof · cited by 0