Theorems · Theorem · measure theory
Real.circleAverage_congr_sphere
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {c : ℂ} {R : ℝ} {f₁ f₂ : ℂ → E},
Set.EqOn f₁ f₂ (Metric.sphere c |R|) → Real.circleAverage f₁ c R = Real.circleAverage f₂ c RIf two functions agree on the circle, then their circle averages agree.
- Cited by
- 9 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
- absstatement and proof · cited by 1,814
- Real.piproof · cited by 1,774
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
- Set.EqOnstatement and proof · cited by 603
- intervalIntegralproof · cited by 546
- Set.uIccproof · cited by 393
- Metric.spherestatement and proof · cited by 371
- circleMapproof · cited by 117
Cited by9
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3
- DiffContOnCl.circleAverageproof · cited by 2
- circleAverage_log_norm_sub_const₀proof · cited by 1
- circleAverage_of_differentiable_on_off_countableproof · cited by 0
- InnerProductSpace.HarmonicOnNhd.circleAverage_poissonKernel_smulproof · cited by 0
- InnerProductSpace.HarmonicContOnCl.circleAverage_poissonKernel_smulproof · cited by 0