Theorems · Theorem · measure theory
Real.circleAverage_const
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] (a : E) (c : ℂ) (R : ℝ),
Real.circleAverage (fun x => a) c R = aThe circle average of a constant function equals the constant.
- Cited by
- 9 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.
Cites14
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
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- CompleteSpacestatement and proof · cited by 2,532
- Real.piproof · cited by 1,774
- one_smulproof · cited by 1,374
- sub_zeroproof · cited by 938
- pow_oneproof · cited by 894
- mul_inv_cancel₀proof · cited by 210
Cited by9
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3
- ValueDistribution.proximity_sum_top_leproof · cited by 2
- Real.circleAverage_mono_on_of_le_circleproof · cited by 2
- Real.circleAverage_nonneg_of_nonnegproof · cited by 1
- circleAverage_log_norm_sub_const_eq_log_radius_add_posLogproof · cited by 1
- Real.circleAverage_const_on_circleproof · cited by 1
- ValueDistribution.proximity_constproof · cited by 0