Theorems · Theorem · potential theory
InnerProductSpace.HarmonicContOnCl.mk_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.HarmonicOnNhd f (Metric.ball x r) →
ContinuousOn f (Metric.closedBall x r) → InnerProductSpace.HarmonicContOnCl f (Metric.ball x r)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 246 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- ContinuousOnstatement and proof · cited by 1,411
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement and proof · cited by 704
- ContinuousOn.monoproof · cited by 156
- InnerProductSpace.HarmonicContOnClstatement · cited by 32
- InnerProductSpace.HarmonicOnNhdstatement and proof · cited by 24
- Metric.closure_ball_subset_closedBallproof · cited by 10
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