Theorems · Theorem · functional analysis

MeasureTheory.Lp.dense_hasCompactSupport_contDiff

∀ {E : Type u_3} {F : Type u_4} [inst : MeasurableSpace E] [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace ℝ E] [FiniteDimensional ℝ E] [BorelSpace E]
  [inst_6 : NormedSpace ℝ F] {μ : MeasureTheory.Measure E} [MeasureTheory.IsFiniteMeasureOnCompacts μ] {p : ENNReal},
  p ≠ ⊤ → ∀ [hp₂ : Fact (1 ≤ p)], Dense {f | ∃ g, ↑↑f =ᵐ[μ] g ∧ HasCompactSupport g ∧ ContDiff ℝ (↑⊤) g}

Defined in

Mathlib.Analysis.Normed.Lp.SmoothApprox

Cited by

0 results in Mathlib

Foundations

Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedAddCommGroupNormedSpaceFiniteDimensionalBorelSpaceNormedSpaceMeasureTheory.IsFiniteMeasureOnCompactsFact