Theorems · Theorem · measure theory
intervalIntegral.integral_comp_mul_left
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b c : ℝ} (f : ℝ → E),
c ≠ 0 → ∫ (x : ℝ) in a..b, f (c * x) = c⁻¹ • ∫ (x : ℝ) in c * a..c * b, f x- Cited by
- 7 results in Mathlib
- Foundations
- Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- mul_commproof · cited by 2,262
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- intervalIntegralstatement and proof · cited by 546
- intervalIntegral.integral_comp_mul_rightproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_comp_mul_addproof · cited by 4
- intervalIntegral.integral_comp_add_mulproof · cited by 3
- Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zeroproof · cited by 3
- intervalIntegral.smul_integral_comp_mul_leftproof · cited by 3
- bernoulliFun_mulproof · cited by 1
- integral_log_sin_zero_pi_div_twoproof · cited by 1
- integral_sin_sq_mul_cos_sqproof · cited by 0