Theorems · Theorem · measure theory
Real.circleAverage_eq_intervalAverage
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℂ → E} {c : ℂ} {R : ℝ},
Real.circleAverage f c R = ⨍ (θ : ℝ) in 0..2 * Real.pi, f (circleMap c R θ)Expression of circleAverage in terms of interval averages.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.pistatement and proof · cited by 1,774
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- sub_zeroproof · cited by 938
- intervalIntegralproof · cited by 546
- mul_inv_revproof · cited by 270
- Set.uIocstatement · cited by 182
- circleMapstatement and proof · cited by 117
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.mahlerMeasure_le_sqrt_sum_sq_norm_coeffproof · cited by 1