Theorems · Theorem · functional analysis

MeasureTheory.eLpNormLESNormFDerivOfLeConst.congr_simp

∀ (F : Type u_6) [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {E : Type u_7} [inst_2 : NormedAddCommGroup E]
  [inst_3 : NormedSpace ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E] [inst_6 : FiniteDimensional ℝ E]
  (μ μ_1 : MeasureTheory.Measure E) (e_μ : μ = μ_1) [inst_7 : μ.IsAddHaarMeasure] [inst_8 : FiniteDimensional ℝ F]
  (s s_1 : Set E),
  s = s_1 →
    ∀ (p p_1 : NNReal),
      p = p_1 →
        ∀ (q q_1 : NNReal),
          q = q_1 →
            MeasureTheory.eLpNormLESNormFDerivOfLeConst F μ s p q =
              MeasureTheory.eLpNormLESNormFDerivOfLeConst F μ_1 s_1 p_1 q_1

Defined in

Mathlib.Analysis.FunctionalSpaces.SobolevInequality

Cited by

1 results in Mathlib

Foundations

Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasureFiniteDimensional