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Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.exists_forall_norm_le

∀ {α : Type u_1} {F : Type u_5} [inst : MeasurableSpace α] [inst_1 : NormedAddCommGroup F]
  (f : MeasureTheory.SimpleFunc α F), ∃ C, ∀ (x : α), ‖f x‖ ≤ C
Defined in
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp
Cited by
3 results in Mathlib
Foundations
Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceNormedAddCommGroup
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Around this declaration

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

MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin · cited by 2MeasureTheory.condExp_str…MeasureTheory.SimpleFunc.memLp_of_isFiniteMeasure · cited by 1SimpleFunc.memLp_of_isFin…MeasureTheory.SimpleFunc.memLp_top · cited by 1SimpleFunc.memLp_topDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceNorm.norm · cited by 5413Norm.normMeasureTheory.SimpleFunc · cited by 411MeasureTheory.SimpleFuncMeasureTheory.SimpleFunc.map · cited by 54SimpleFunc.mapMeasureTheory.SimpleFunc.exists_forall_le · cited by 2SimpleFunc.exists_forall_…SimpleFunc.exists_forall_norm…CITED BYCITES

Cites8

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

Cited by3

Results whose statement or proof uses this declaration.