Theorems · Theorem · measure theory
MeasureTheory.Lp.simpleFunc.add_toSimpleFunc
∀ {α : Type u_1} {E : Type u_4} [inst : MeasurableSpace α] [inst_1 : NormedAddCommGroup E] {p : ENNReal}
{μ : MeasureTheory.Measure α} (f g : ↥(MeasureTheory.Lp.simpleFunc E p μ)),
⇑(MeasureTheory.Lp.simpleFunc.toSimpleFunc (f + g)) =ᵐ[μ]
⇑(MeasureTheory.Lp.simpleFunc.toSimpleFunc f) + ⇑(MeasureTheory.Lp.simpleFunc.toSimpleFunc g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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 · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.L1.SimpleFunc.setToL1S_addproof · cited by 2