Theorems · Theorem · measure theory
MeasureTheory.AEEqFun.coeFn_sup
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace β]
[inst_2 : SemilatticeSup β] [inst_3 : ContinuousSup β] (f g : α →ₘ[μ] β), ↑(f ⊔ g) =ᵐ[μ] fun x => ↑f x ⊔ ↑g x- Defined in
- Mathlib.MeasureTheory.Function.AEEqFun
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- SemilatticeSupstatement and proof · cited by 785
- MeasureTheory.AEEqFun.caststatement · cited by 380
- ContinuousSupstatement and proof · cited by 70
- MeasureTheory.AEEqFun.coeFn_comp₂proof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.AEEqFun.coeFn_absproof · cited by 1
- MeasureTheory.AEEqFun.sup_leproof · cited by 0
- MeasureTheory.Lp.coeFn_supproof · cited by 0
- MeasureTheory.AEEqFun.le_sup_leftproof · cited by 0
- MeasureTheory.AEEqFun.le_sup_rightproof · cited by 0