Theorems · Definition · functional analysis
MeasureTheory.lintegralPowLePowLIntegralFDerivConst
{E : Type u_5} →
[inst : NormedAddCommGroup E] →
[inst_1 : NormedSpace ℝ E] →
[inst_2 : MeasurableSpace E] →
[BorelSpace E] → [FiniteDimensional ℝ E] → (μ : MeasureTheory.Measure E) → [μ.IsAddHaarMeasure] → ℝ → NNRealThe constant factor occurring in the conclusion of lintegral_pow_le_pow_lintegral_fderiv.
It only depends on E, μ and p.
It is determined by the ratio of the measures on E and ℝⁿ and
the operator norm of a chosen equivalence E ≃ ℝⁿ (raised to suitable powers involving p).
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement · cited by 15,752
- MeasurableSpacestatement · cited by 13,106
- NormedSpacestatement · cited by 12,499
- MeasureTheory.Measurestatement · cited by 10,939
- NNRealstatement · cited by 4,310
- FiniteDimensionalstatement · cited by 1,854
- BorelSpacestatement · cited by 1,602
- MeasureTheory.Measure.IsAddHaarMeasurestatement · cited by 255
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNormLESNormFDerivOneConst_defstatement and proof · cited by 1
- MeasureTheory.lintegralPowLePowLIntegralFDerivConst_defstatement · cited by 1
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderivstatement and proof · cited by 1
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_oneproof · cited by 1
- MeasureTheory.lintegralPowLePowLIntegralFDerivConst.congr_simpstatement and proof · cited by 0