Theorems · Theorem · measure theory
intervalIntegral.integral_comp_add_left
∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} (f : ℝ → E) (d : ℝ),
∫ (x : ℝ) in a..b, f (d + x) = ∫ (x : ℝ) in d + a..d + b, f x- Cited by
- 2 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
- add_commproof · cited by 1,535
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- intervalIntegralstatement and proof · cited by 546
- intervalIntegral.integral_comp_add_rightproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_comp_add_mulproof · cited by 3
- circleAverage_log_norm_sub_const₁proof · cited by 1