Theorems · Theorem · measure theory

MeasureTheory.IntegrableOn.continuousOn_Iic_primitive_Iio

∀ {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.Iio a₀) μ → ContinuousOn (fun b => ∫ (x : ℝ) in Set.Iio b, f x ∂μ) (Set.Iic a₀)

Defined in: Mathlib.MeasureTheory.Integral.DominatedConvergence
Cited by: 1 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasureTheory.NullSingletonClass

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
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 and proof · cited by 1,779
Set.Iccproof · cited by 1,702
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
ContinuousOnstatement · cited by 1,411
Set.Iiostatement and proof · cited by 1,166
Set.Iicstatement and proof · cited by 1,111
MeasureTheory.IntegrableOnstatement and proof · cited by 548

Cited by1

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MeasureTheory.IntegrableOn.continuousOn_Iic_primitive_Iicproof · cited by 0