Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.piecewise_same
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (f : MeasureTheory.SimpleFunc α β) {s : Set α}
(hs : MeasurableSet s), MeasureTheory.SimpleFunc.piecewise s hs f f = f- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.piecewisestatement · cited by 26
- MeasureTheory.SimpleFunc.coe_injectiveproof · cited by 5
- Set.piecewise_sameproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- MeasureTheory.MemLp.induction_denseproof · cited by 2
- MeasureTheory.Lp.simpleFunc.inductionproof · cited by 2
- MeasureTheory.MemLp.inductionproof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_indicatorproof · cited by 1
- MeasureTheory.SimpleFunc.exists_upperSemicontinuous_le_lintegral_leproof · cited by 1