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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.Integrable.neg_vectorMeasure

∀ {X : Type u_2} {E : Type u_4} {F : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] {f : X → E} {μ : MeasureTheory.VectorMeasure X F}, μ.Integrable f → (-μ).Integrable f
Defined in
Mathlib.MeasureTheory.VectorMeasure.Integral
Cited by
2 results in Mathlib
Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedAddCommGroup
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Around this declaration

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

MeasureTheory.VectorMeasure.integral_sub_vectorMeasure · cited by 0VectorMeasure.integral_su…MeasureTheory.VectorMeasure.Integrable.sub_vectorMeasure · cited by 0Integrable.sub_vectorMeas…NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.variation · cited by 125VectorMeasure.variationMeasureTheory.VectorMeasure.Integrable · cited by 63VectorMeasure.IntegrableMeasureTheory.Integrable.mono_measure · cited by 26Integrable.mono_measureMeasureTheory.VectorMeasure.variation_neg · cited by 3VectorMeasure.variation_n…Integrable.neg_vectorMeasureCITED BYCITES

Cites7

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Cited by2

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