Theorems · Theorem · measure theory

Real.circleAverage_fun_add

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {c : ℂ} {R : ℝ} {f₁ f₂ : ℂ → E},
  CircleIntegrable f₁ c R →
    CircleIntegrable f₂ c R →
      Real.circleAverage (fun z => f₁ z + f₂ z) c R = Real.circleAverage f₁ c R + Real.circleAverage f₂ c R

Circle averages commute with addition.

Defined in: Mathlib.MeasureTheory.Integral.CircleAverage
Cited by: 1 results in Mathlib
Foundations: Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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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
NormedSpacestatement and proof · cited by 12,499
Complexstatement and proof · cited by 5,565
Real.circleAveragestatement · cited by 106
CircleIntegrablestatement and proof · cited by 86
Real.circleAverage_addproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3