Theorems · Theorem · measure theory
MeasureTheory.LocallyIntegrable.indicator
∀ {X : Type u_1} {ε'' : Type u_5} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X]
[inst_2 : TopologicalSpace ε''] [inst_3 : ESeminormedAddMonoid ε''] {μ : MeasureTheory.Measure X} {f : X → ε''},
MeasureTheory.LocallyIntegrable f μ →
∀ {s : Set X}, MeasurableSet s → MeasureTheory.LocallyIntegrable (s.indicator f) μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- nhdsproof · cited by 5,554
- MeasurableSetstatement and proof · cited by 3,075
- Set.indicatorstatement · cited by 723
- MeasureTheory.IntegrableOnproof · cited by 548
- ESeminormedAddMonoidstatement and proof · cited by 133
- MeasureTheory.LocallyIntegrablestatement and proof · cited by 90
- MeasureTheory.IntegrableOn.indicatorproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ExistsContDiffBumpBase.y_pos_of_mem_ballproof · cited by 1
- ExistsContDiffBumpBase.y_smoothproof · cited by 0