Theorems · Theorem · functional analysis

TemperedDistribution.MemSobolev.congr_simp

∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
  [inst_2 : InnerProductSpace ℝ E] [inst_3 : FiniteDimensional ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E]
  [inst_6 : NormedSpace ℂ F] [inst_7 : CompleteSpace F] (s s_1 : ℝ),
  s = s_1 →
    ∀ (p p_1 : ENNReal) (e_p : p = p_1) [hp : Fact (1 ≤ p)] (f f_1 : TemperedDistribution E F),
      f = f_1 → TemperedDistribution.MemSobolev s p f = TemperedDistribution.MemSobolev s_1 p_1 f_1

Defined in

Mathlib.Analysis.Distribution.Sobolev

Cited by

0 results in Mathlib

Foundations

Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupInnerProductSpaceFiniteDimensionalMeasurableSpaceBorelSpaceNormedSpaceCompleteSpaceFact