Theorems · Theorem · measure theory

MeasureTheory.integrable_const_iff_isFiniteMeasure

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {c : β}, c ≠ 0 → (MeasureTheory.Integrable (fun x => c) μ ↔ MeasureTheory.IsFiniteMeasure μ)

Defined in: Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by: 2 results in Mathlib
Foundations: Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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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
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Top.topproof · cited by 9,680
Set.univproof · cited by 3,945
MeasureTheory.Integrablestatement · cited by 1,367
MeasureTheory.IsFiniteMeasurestatement · cited by 1,078

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.integral_constproof · cited by 75
ProbabilityTheory.condVar_constproof · cited by 0