Theorems · Theorem · measure theory
Real.circleAverage_eq_circleIntegral
∀ {c : ℂ} {R : ℝ} {F : Type u_4} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℂ F] {f : ℂ → F},
R ≠ 0 → Real.circleAverage f c R = (2 * ↑Real.pi * Complex.I)⁻¹ • ∮ (z : ℂ) in C(c, R), (z - c)⁻¹ • f zExpression of the circleAverage in terms of a circleIntegral.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- MeasureTheory.Measureproof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
Cited by1
Results whose statement or proof uses this declaration.
- circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countableproof · cited by 2