Theorems · Theorem · measure theory
intervalIntegral.integral_indicator
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {μ : MeasureTheory.Measure ℝ}
{a₁ a₂ a₃ : ℝ}, a₂ ∈ Set.Icc a₁ a₃ → ∫ (x : ℝ) in a₁..a₃, {x | x ≤ a₂}.indicator f x ∂μ = ∫ (x : ℝ) in a₁..a₂, f x ∂μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 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
- 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
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- MeasureTheory.integralproof · cited by 1,779
- Set.Iccstatement and proof · cited by 1,702
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Set.Iocproof · cited by 971
- Set.indicatorstatement and proof · cited by 723
Cited by1
Results whose statement or proof uses this declaration.
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6