Theorems · Theorem · measure theory

Real.circleAverage_fun_sub

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f₁ f₂ : ℂ → E} {c : ℂ} {R : ℝ},
  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 subtraction.

Defined in: Mathlib.MeasureTheory.Integral.CircleAverage
Cited by: 0 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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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_subproof · cited by 3

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