Theorems · Theorem · functional analysis

MeasureTheory.Lp.dist_def

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] (f g : ↥(MeasureTheory.Lp E p μ)),
  dist f g = (MeasureTheory.eLpNorm (↑↑f - ↑↑g) p μ).toReal

Defined in: Mathlib.MeasureTheory.Function.LpSpace.Basic
Cited by: 7 results in Mathlib
Foundations: Depth 224 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 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
ENNRealstatement and proof · cited by 9,879
AddSubgroupstatement · cited by 3,232
Dist.diststatement · cited by 1,539
sub_eq_add_negproof · cited by 1,023
neg_negproof · cited by 960
ENNReal.toRealstatement and proof · cited by 859
MeasureTheory.AEEqFunstatement and proof · cited by 856
MeasureTheory.Lpstatement and proof · cited by 715

Cited by7

Results whose statement or proof uses this declaration.

MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'proof · cited by 5
SchwartzMap.denseRange_toLpCLMproof · cited by 3
MeasureTheory.Lp.edist_distproof · cited by 2
MeasureTheory.continuous_L1_toL1proof · cited by 1
MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNormproof · cited by 0
MeasureTheory.Lp.dense_hasCompactSupport_contDiffproof · cited by 0
MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNormproof · cited by 0