Theorems · Theorem · measure theory
intervalIntegral.integral_congr_codiscreteWithin
∀ {a b : ℝ} {f₁ f₂ : ℝ → ℝ},
f₁ =ᶠ[Filter.codiscreteWithin (Set.uIoc a b)] f₂ → ∫ (x : ℝ) in a..b, f₁ x = ∫ (x : ℝ) in a..b, f₂ xIntegrals are invariant when functions change along discrete sets.
- Cited by
- 2 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.
Cites10
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
- Set.ofPredproof · cited by 6,101
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- intervalIntegralstatement · cited by 546
- Set.uIocstatement and proof · cited by 182
- Filter.codiscreteWithinstatement and proof · cited by 87
- measurableSet_uIocproof · cited by 20
- intervalIntegral.integral_congr_ae_restrictproof · cited by 6
- ae_restrict_le_codiscreteWithinproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- integral_log_sin_zero_pi_div_twoproof · cited by 1
- intervalAverage_congr_codiscreteWithinproof · cited by 0