Theorems · Theorem · measure theory
MeasureTheory.L1.dist_eq_integral_dist
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {H : Type u_6} [inst : NormedAddCommGroup H]
(f g : ↥(MeasureTheory.Lp H 1 μ)), dist f g = ∫ (a : α), dist (↑↑f a) (↑↑g a) ∂μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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
- ENNRealstatement · cited by 9,879
- Norm.normproof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.integralstatement and proof · cited by 1,779
- Dist.diststatement · cited by 1,539
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement and proof · cited by 380
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