Theorems · Theorem · measure theory
MeasureTheory.AEEqFun.coeFn_mk
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace β]
(f : α → β) (hf : MeasureTheory.AEStronglyMeasurable f μ), ↑(MeasureTheory.AEEqFun.mk f hf) =ᵐ[μ] f- Defined in
- Mathlib.MeasureTheory.Function.AEEqFun
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.AEEqFunproof · cited by 856
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.AEEqFun.mkstatement and proof · cited by 62
- MeasureTheory.AEEqFun.mk_coeFnproof · cited by 11
- MeasureTheory.AEEqFun.mk_eq_mkproof · cited by 5
Cited by18
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.coeFn_toLpproof · cited by 35
- MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFunproof · cited by 11
- MeasureTheory.Integrable.coeFn_toL1proof · cited by 11
- MeasureTheory.AEEqFun.coeFn_compproof · cited by 8
- ContinuousMap.coeFn_toAEEqFunproof · cited by 6
- MeasureTheory.AEEqFun.coeFn_comp₂proof · cited by 6
- MeasureTheory.AEEqFun.coeFn_compQuasiMeasurePreservingproof · cited by 5
- MeasureTheory.eLpNorm_aeeqFunproof · cited by 4
- MeasureTheory.AEEqFun.coeFn_constproof · cited by 4
- MeasureTheory.AEEqFun.integrable_mkproof · cited by 3
- ContinuousMap.coeFn_toLpproof · cited by 3
- MeasureTheory.L2.integrable_innerproof · cited by 2