Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.support_indicator

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : Zero β] {s : Set α} (hs : MeasurableSet s)
  (f : MeasureTheory.SimpleFunc α β),
  Function.support ⇑(MeasureTheory.SimpleFunc.piecewise s hs f (MeasureTheory.SimpleFunc.const α 0)) =
    s ∩ Function.support ⇑f

Defined in: Mathlib.MeasureTheory.Function.SimpleFunc
Cited by: 1 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace Zero

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · 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
Function.supportstatement · cited by 610
MeasureTheory.SimpleFuncstatement and proof · cited by 411
MeasureTheory.SimpleFunc.conststatement · cited by 50
MeasureTheory.SimpleFunc.piecewisestatement · cited by 26
Set.support_indicatorproof · cited by 10

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.SimpleFunc.measure_lt_top_of_memLp_indicatorproof · cited by 3