Theorems · Theorem · measure theory
MeasureTheory.IntegrableOn.continuousOn_Ici_primitive_Ici
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {μ : MeasureTheory.Measure ℝ} {f : ℝ → E}
[MeasureTheory.NullSingletonClass μ] {a₀ : ℝ},
MeasureTheory.IntegrableOn f (Set.Ici a₀) μ → ContinuousOn (fun b => ∫ (x : ℝ) in Set.Ici b, f x ∂μ) (Set.Ici a₀)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- ContinuousOnstatement and proof · cited by 1,411
- Set.Icistatement and proof · cited by 1,070
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- MeasureTheory.NullSingletonClassstatement and proof · cited by 125
- MeasureTheory.IntegrableOn.mono_setproof · cited by 60
- Set.Ioi_subset_Ici_selfproof · cited by 34
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