Theorems · Theorem · measure theory

MeasureTheory.integrable_comp_mul_left_iff

∀ {F : Type u_1} [inst : NormedAddCommGroup F] (g : ℝ → F) {R : ℝ},
  R ≠ 0 →
    (MeasureTheory.Integrable (fun x => g (R * x)) MeasureTheory.volume ↔
      MeasureTheory.Integrable g MeasureTheory.volume)

Defined in: Mathlib.MeasureTheory.Measure.Haar.NormedSpace
Cited by: 3 results in Mathlib
Foundations: Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites5

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

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasureTheory.Integrablestatement · cited by 1,367
MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
MeasureTheory.integrable_comp_smul_iffproof · cited by 2

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.integrableOn_Ioi_comp_mul_left_iffproof · cited by 5
MeasureTheory.integrable_comp_mul_right_iffproof · cited by 2
MeasureTheory.Integrable.comp_mul_left'proof · cited by 0