Theorems · Theorem · measure theory
MeasureTheory.preVariation.exists_Finpartition_sum_gt
∀ {X : Type u_1} [inst : MeasurableSpace X] (f : Set X → ENNReal) {s : Set X} (hs : MeasurableSet s) {a : ENNReal},
a < MeasureTheory.preVariationFun f s → ∃ P, a < ∑ p ∈ P.parts, f ↑p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- MeasurableSetstatement and proof · cited by 3,075
- Finpartitionstatement · cited by 199
- Finpartition.partsstatement · cited by 184
- MeasureTheory.preVariationFunstatement and proof · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.preVariation.exists_Finpartition_sum_geproof · cited by 2
- MeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variationproof · cited by 1