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Theorems · Theorem · measure theory

MeasureTheory.MemLp.fst

∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {p : ENNReal} {E : Type u_2} {F : Type u_3}
  [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] {f : X → E × F},
  MeasureTheory.MemLp f p μ → MeasureTheory.MemLp (fun x => (f x).1) p μ
Defined in
Mathlib.MeasureTheory.SpecificCodomains.Pi
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Foundations
Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedAddCommGroup
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NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.MemLp · cited by 457MeasureTheory.MemLpMeasureTheory.memLp_prod_iff · cited by 3MeasureTheory.memLp_prod_…MemLp.fstCITED BYCITES

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