Theorems · Theorem · functional analysis

MeasureTheory.memLp_of_bounded

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ] {a b : ℝ}
  {f : α → ℝ},
  (∀ᵐ (x : α) ∂μ, f x ∈ Set.Icc a b) →
    MeasureTheory.AEStronglyMeasurable f μ → ∀ (p : ENNReal), MeasureTheory.MemLp f p μ

Defined in: Mathlib.MeasureTheory.Function.LpSeminorm.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure

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Cites18

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

Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Filter.Eventuallystatement and proof · cited by 3,134
MeasureTheory.aestatement and proof · cited by 2,352
absproof · cited by 1,814
Set.Iccstatement and proof · cited by 1,702
Filter.univ_mem'proof · cited by 1,672
Filter.mp_memproof · cited by 1,537
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.variance_le_sub_mul_subproof · cited by 1