Theorems · Theorem · measure theory
Real.circleAverage_abs_radius
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℂ → E} {c : ℂ} {R : ℝ},
Real.circleAverage f c |R| = Real.circleAverage f c RCircle averages do not change when replacing the radius by its absolute value.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 1,814
- abs_of_nonnegproof · cited by 279
- Real.circleAveragestatement and proof · cited by 106
- abs_of_negproof · cited by 39
- Real.circleAverage_neg_radiusproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countableproof · cited by 2
- InnerProductSpace.HarmonicContOnCl.circleAverage_eqproof · cited by 1