Theorems · Theorem · measure theory
Real.circleAverage_add
∀ {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 (f₁ + f₂) c R = Real.circleAverage f₁ c R + Real.circleAverage f₂ c RCircle averages commute with addition.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.piproof · cited by 1,774
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- intervalIntegralproof · cited by 546
- smul_addproof · cited by 263
- circleMapproof · cited by 117
- Real.circleAveragestatement and proof · cited by 106
- CircleIntegrablestatement and proof · cited by 86
- intervalIntegral.integral_addproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- ValueDistribution.proximity_mul_top_leproof · cited by 2
- ValueDistribution.proximity_sum_top_leproof · cited by 2
- circleAverage_log_norm_sub_const_eq_log_radius_add_posLogproof · cited by 1
- Real.circleAverage_fun_addproof · cited by 1