Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.enorm_le_totalVariation
∀ {X : Type u_1} {mX : MeasurableSpace X} (s : MeasureTheory.SignedMeasure X) (i : Set X), ‖s i‖ₑ ≤ s.totalVariation iThe pointwise bound ‖s i‖ₑ ≤ s.totalVariation i for any signed measure.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- ENNReal.ofRealproof · cited by 863
- ENorm.enormstatement · cited by 715
- MeasureTheory.measure_ne_topproof · cited by 171
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.measureReal_defproof · cited by 68
- ENNReal.ofReal_toRealproof · cited by 65
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.totalVariation_eq_variationproof · cited by 0