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MeasureTheory.eLpNorm_add_lt_top

∀ {α : Type u_1} {ε : Type u_3} {m : MeasurableSpace α} [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddMonoid ε]
  {p : ENNReal} {μ : MeasureTheory.Measure α} {f g : α → ε},
  MeasureTheory.MemLp f p μ → MeasureTheory.MemLp g p μ → MeasureTheory.eLpNorm (f + g) p μ < ⊤
Defined in
Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality
Cited by
2 results in Mathlib
Foundations
Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceESeminormedAddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MeasureTheory.MemLp.add · cited by 24MemLp.addMeasureTheory.SimpleFunc.memLp_approxOn · cited by 3SimpleFunc.memLp_approxOnTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topMeasureTheory.MemLp · cited by 457MeasureTheory.MemLpMeasureTheory.eLpNorm · cited by 329MeasureTheory.eLpNormESeminormedAddMonoid · cited by 133ESeminormedAddMonoidENNReal.mul_lt_top · cited by 41ENNReal.mul_lt_topMeasureTheory.MemLp.aestronglyMeasurable · cited by 30MemLp.aestronglyMeasurableENNReal.add_lt_top · cited by 27ENNReal.add_lt_topMeasureTheory.eLpNorm_add_le' · cited by 3MeasureTheory.eLpNorm_add…ENNReal.LpAddConst_lt_top · cited by 2ENNReal.LpAddConst_lt_topMeasureTheory.eLpNorm_add_lt_…CITED BYCITES

Cites13

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Cited by2

Results whose statement or proof uses this declaration.