Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.enorm_measure_le_variation
∀ {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) (E : Set X), ‖μ E‖ₑ ≤ μ.variation E- Cited by
- 15 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Bot.botproof · cited by 4,720
- MeasurableSetproof · cited by 3,075
- Finset.sum_congrproof · cited by 2,323
- T2Spacestatement and proof · cited by 1,351
- ENorm.enormstatement and proof · cited by 715
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.variation_restrictproof · cited by 14
- MeasureTheory.VectorMeasure.variation_add_leproof · cited by 4
- MeasureTheory.VectorMeasure.variation_transpose_leproof · cited by 4
- MeasurableEmbedding.variation_mapproof · cited by 3
- MeasureTheory.VectorMeasure.variation_diracproof · cited by 2
- MeasureTheory.VectorMeasure.norm_measure_le_variationproof · cited by 2
- MeasureTheory.VectorMeasure.enorm_apply_le_semivariationproof · cited by 2
- MeasureTheory.Measure.variation_toSignedMeasureproof · cited by 2
- MeasureTheory.VectorMeasure.variation_apply_eq_zeroproof · cited by 1
- MeasureTheory.VectorMeasure.variation_eq_zeroproof · cited by 1
- MeasureTheory.VectorMeasure.variation_transpose_eq_smulproof · cited by 1
- MeasureTheory.VectorMeasure.absolutelyContinuousproof · cited by 0