Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.variation_restrict_le
∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
[inst_2 : T2Space V] {μ : MeasureTheory.VectorMeasure X V} {s : Set X},
(μ.restrict s).variation ≤ μ.variation.restrict s- Cited by
- 5 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- MeasureTheory.Measurestatement · cited by 10,939
- MeasurableSetproof · cited by 3,075
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- T2Spacestatement and proof · cited by 1,351
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.VectorMeasure.restrictstatement and proof · cited by 139
- MeasureTheory.VectorMeasure.variationstatement and proof · cited by 125
- ENormedAddCommMonoidstatement and proof · cited by 32
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.tendsto_setIntegral_of_L1proof · cited by 1
- MeasureTheory.VectorMeasure.IntegrableOn.unionproof · cited by 1
- MeasureTheory.VectorMeasure.Integrable.tendsto_setIntegral_nhds_zeroproof · cited by 0
- MeasureTheory.VectorMeasure.enorm_setIntegral_le_lintegral_enormproof · cited by 0