Theorems · Theorem · real analysis
BoxIntegral.HasIntegral.smul
∀ {ι : Type u} {E : Type v} {F : Type w} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {I : BoxIntegral.Box ι} [inst_4 : Fintype ι]
{l : BoxIntegral.IntegrationParams} {f : (ι → ℝ) → E} {vol : BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤} {y : F},
BoxIntegral.HasIntegral I l f vol y → ∀ (c : ℝ), BoxIntegral.HasIntegral I l (c • f) vol (c • y)- Defined in
- Mathlib.Analysis.BoxIntegral.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 167 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.
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- nhdsproof · cited by 5,554
- ContinuousLinearMapstatement and proof · cited by 5,352
- Filter.Tendstoproof · cited by 3,814
- WithTopstatement · cited by 3,754
- BoxIntegral.Boxstatement and proof · cited by 464
- tendsto_const_nhdsproof · cited by 330
Cited by2
Results whose statement or proof uses this declaration.
- BoxIntegral.Integrable.smulproof · cited by 1
- BoxIntegral.integral_smulproof · cited by 0