Theorems · Theorem · measure theory

MeasureTheory.Integrable.smul_of_top_right

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {𝕜 : Type u_8} [inst_1 : NormedRing 𝕜] [inst_2 : Module 𝕜 β] [IsBoundedSMul 𝕜 β] {f : α → β} {φ : α → 𝕜},
  MeasureTheory.Integrable f μ → MeasureTheory.MemLp φ ⊤ μ → MeasureTheory.Integrable (φ • f) μ

Defined in: Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by: 5 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedRing Module IsBoundedSMul

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Cites12

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

Modulestatement and proof · cited by 20,661
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Top.topstatement and proof · cited by 9,680
MeasureTheory.Integrablestatement and proof · cited by 1,367
NormedRingstatement and proof · cited by 924
MeasureTheory.MemLpstatement and proof · cited by 457
IsBoundedSMulstatement and proof · cited by 329
MeasureTheory.memLp_one_iff_integrableproof · cited by 73
MeasureTheory.MemLp.smulproof · cited by 13

Cited by5

Results whose statement or proof uses this declaration.

MeasureTheory.Integrable.bdd_smulproof · cited by 4
integrableOn_peak_smul_of_integrableOn_of_tendstoproof · cited by 2
MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_subproof · cited by 1
MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupportproof · cited by 1
MeasureTheory.Integrable.mul_of_top_rightproof · cited by 0