Theorems · Theorem · measure theory
intervalIntegral.integral_comp_sub_mul
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b c : ℝ} (f : ℝ → E),
c ≠ 0 → ∀ (d : ℝ), ∫ (x : ℝ) in a..b, f (d - c * x) = c⁻¹ • ∫ (x : ℝ) in d - c * b..d - c * a, f x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.MeasureSpace.volumestatement and proof · cited by 1,323
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- intervalIntegralstatement and proof · cited by 546
- neg_smulproof · cited by 306
- smul_negproof · cited by 181
- neg_ne_zeroproof · cited by 70
- inv_negproof · cited by 42
- intervalIntegral.integral_symmproof · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_comp_sub_leftproof · cited by 4
- intervalIntegral.smul_integral_comp_sub_mulproof · cited by 1
- intervalIntegral.integral_comp_sub_divproof · cited by 1