Theorems · Theorem · functional analysis
MeasureTheory.Lp.zero_smul
∀ {α : Type u_1} (𝕜 : Type u_3) {E : Type u_4} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (p : ENNReal)
{q r : ENNReal} [hpqr : p.HolderTriple q r] [inst : NormedRing 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : Module 𝕜 E] [inst_3 : IsBoundedSMul 𝕜 E] (f : ↥(MeasureTheory.Lp E q μ)), 0 • f = 0- Defined in
- Mathlib.MeasureTheory.Function.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- 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
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- NormedRingstatement and proof · cited by 924
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- zero_smulproof · cited by 716
- MeasureTheory.Lpstatement and proof · cited by 715
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.neg_smulproof · cited by 1