Theorems · Theorem · functional analysis

MeasureTheory.SNormLESNormFDerivOfEqConst_def

∀ (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 : MeasureTheory.Measure E) [inst_7 : μ.IsAddHaarMeasure] [inst_8 : FiniteDimensional ℝ F] (p : ℝ),
  MeasureTheory.SNormLESNormFDerivOfEqConst F μ p =
    let F' := EuclideanSpace ℝ (Fin (Module.finrank ℝ F));
    have e := toEuclidean;
    ‖↑e.symm‖₊ * MeasureTheory.eLpNormLESNormFDerivOfEqInnerConst μ p * ‖↑e‖₊

Defined in

Mathlib.Analysis.FunctionalSpaces.SobolevInequality

Cited by

1 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasureFiniteDimensional