Theorems · Theorem · functional analysis
MeasureTheory.Lp.ext_iff
∀ {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)}, f = g ↔ ↑↑f =ᵐ[μ] ↑↑g- Cited by
- 5 results in Mathlib
- Foundations
- Depth 222 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.
Cites12
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 and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement and proof · cited by 380
- Filter.EventuallyEq.reflproof · cited by 108
- MeasureTheory.Lp.extproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.aestronglyMeasurable_condExpL1proof · cited by 5
- MeasureTheory.Lp.eq_zero_iff_ae_eq_zeroproof · cited by 2
- ProbabilityTheory.uncenteredCovarianceBilinDual_zeroproof · cited by 2
- MeasureTheory.nontrivial_Lp_real_of_nontrivial_Lpproof · cited by 1
- MeasureTheory.tendsto_condExp_uniqueproof · cited by 1