Theorems · Theorem · potential theory
InnerProductSpace.HarmonicContOnCl.continuousOn_ball
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
{F : Type u_2} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] {f : E → F} {x : E} {r : ℝ},
InnerProductSpace.HarmonicContOnCl f (Metric.ball x r) → ContinuousOn f (Metric.closedBall x r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 164 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.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- ContinuousOnstatement and proof · cited by 1,411
- eq_or_neproof · cited by 1,117
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement · cited by 704
- InnerProductSpace.HarmonicContOnClstatement and proof · cited by 32
- closure_ballproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicContOnCl.circleAverage_eqproof · cited by 1