Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.integrable_indicator_iff
∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
[inst_1 : NormedAddCommGroup F] {μ : MeasureTheory.VectorMeasure X F} {f : X → E} {s : Set X},
MeasurableSet s → (μ.Integrable (s.indicator f) ↔ μ.IntegrableOn f s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.Integrableproof · cited by 1,367
- T2Spaceproof · cited by 1,351
- Set.indicatorstatement · cited by 723
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- ESeminormedAddMonoidproof · cited by 133
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.integral_indicatorproof · cited by 7
- MeasureTheory.VectorMeasure.IntegrableOn.integrable_indicatorproof · cited by 2