Theorems · Theorem · functional analysis
MeasureTheory.Lp.coeFn_le
∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p : ENNReal}
[inst : NormedAddCommGroup E] [inst_1 : PartialOrder E] (f g : ↥(MeasureTheory.Lp E p μ)), ↑↑f ≤ᵐ[μ] ↑↑g ↔ f ≤ g- Defined in
- Mathlib.MeasureTheory.Function.LpOrder
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
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
- PartialOrderstatement and proof · cited by 6,410
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- Filter.EventuallyLEstatement and proof · cited by 383
- MeasureTheory.AEEqFun.caststatement and proof · cited by 380
- Subtype.coe_le_coeproof · cited by 20
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.coeFn_nonnegproof · cited by 2
- MeasureTheory.condExpInd_nonnegproof · cited by 1
- MeasureTheory.Lp.simpleFunc.coeFn_leproof · cited by 1
- MeasureTheory.condExpL1_monoproof · cited by 1