Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.isSigmaSubadditiveSetFun_enorm
∀ {X : Type u_1} {mX : MeasurableSpace X} {V : Type u_2} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
[T2Space V] (μ : MeasureTheory.VectorMeasure X V), MeasureTheory.IsSigmaSubadditiveSetFun fun x => ‖μ x‖ₑThe norm of a vector measure is σ-subadditive on measurable sets.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidproof · cited by 12,281
- MeasurableSetproof · cited by 3,075
- Disjointproof · cited by 2,201
- SummationFilter.unconditionalproof · cited by 2,068
- T2Spacestatement and proof · cited by 1,351
- tsumproof · cited by 1,148
- ENorm.enormstatement and proof · cited by 715
- Function.onFunproof · cited by 570
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.variationproof · cited by 125
- MeasureTheory.VectorMeasure.enorm_measure_le_variationproof · cited by 15
- MeasureTheory.VectorMeasure.variation_zeroproof · cited by 9
- MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_leproof · cited by 3
- MeasureTheory.VectorMeasure.variation_negproof · cited by 3
- MeasureTheory.VectorMeasure.exists_variation_le_add'proof · cited by 2
- MeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variationproof · cited by 1
- MeasureTheory.VectorMeasure.le_variationproof · cited by 1
- MeasureTheory.VectorMeasure.variation_eq_ennrealToMeasureproof · cited by 1
- MeasureTheory.VectorMeasure.variation_applystatement · cited by 0