Theorems · Theorem · functional analysis

MeasureTheory.lintegralPowLePowLIntegralFDerivConst.congr_simp

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E]
  [inst_3 : BorelSpace E] [inst_4 : FiniteDimensional ℝ E] (μ μ_1 : MeasureTheory.Measure E) (e_μ : μ = μ_1)
  [inst_5 : μ.IsAddHaarMeasure] (p p_1 : ℝ),
  p = p_1 →
    MeasureTheory.lintegralPowLePowLIntegralFDerivConst μ p =
      MeasureTheory.lintegralPowLePowLIntegralFDerivConst μ_1 p_1

Defined in: Mathlib.Analysis.FunctionalSpaces.SobolevInequality
Cited by: 0 results in Mathlib
Foundations: Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace FiniteDimensional MeasureTheory.Measure.IsAddHaarMeasure

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Realstatement and proof · cited by 25,697
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
NNRealstatement · cited by 4,310
FiniteDimensionalstatement and proof · cited by 1,854
BorelSpacestatement and proof · cited by 1,602
MeasureTheory.Measure.IsAddHaarMeasurestatement and proof · cited by 255
MeasureTheory.lintegralPowLePowLIntegralFDerivConststatement and proof · cited by 5

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