Theorems · Theorem · functional analysis
MeasureTheory.Lp.eq_zero_iff_ae_eq_zero
∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
[inst : NormedAddCommGroup E] {f : ↥(MeasureTheory.Lp E p μ)}, f = 0 ↔ ↑↑f =ᵐ[μ] 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 223 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.
Cites13
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
- MeasureTheory.Lp.ext_iffproof · cited by 5
- MeasureTheory.AEEqFun.coeFn_zeroproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzWith.compLp_zeroproof · cited by 1
- MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_botproof · cited by 0