Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ

∀ {α : Type u_1} {ε : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ε}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {p q : ENNReal},
  p ≤ q →
    MeasureTheory.AEStronglyMeasurable f μ →
      MeasureTheory.eLpNorm f p μ ≤ MeasureTheory.eLpNorm f q μ * μ Set.univ ^ (1 / p.toReal - 1 / q.toReal)

Defined in: Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp
Cited by: 3 results in Mathlib
Foundations: Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace ContinuousENorm

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites38

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Top.topproof · cited by 9,680
Set.univstatement and proof · cited by 3,945
mul_oneproof · cited by 3,885
LE.le.transproof · cited by 3,151
eq_or_neproof · cited by 1,117

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_leproof · cited by 1
MeasureTheory.eLpNorm_le_eLpNorm_of_exponent_leproof · cited by 0
MeasureTheory.summable_norm_of_tsum_eLpNorm_ne_topproof · cited by 0