Theorems · Theorem · measure theory
MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure
∀ {α : Type u_1} [inst : TopologicalSpace α] [NormalSpace α] [inst_2 : MeasurableSpace α] [inst_3 : BorelSpace α]
(E : Type u_2) [inst_4 : NormedAddCommGroup E] (μ : MeasureTheory.Measure α) {p : ENNReal} [NormedSpace ℝ E]
[inst_6 : SecondCountableTopologyEither α E] [inst_7 : Fact (1 ≤ p)],
p ≠ ⊤ → ∀ [μ.WeaklyRegular], (MeasureTheory.Lp.boundedContinuousFunction E p μ).topologicalClosure = ⊤A function in Lp can be approximated in Lp by continuous functions.
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- Foundations
- Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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
- TopologicalSpacestatement and proof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.AEEqFunstatement · cited by 856
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