Const smul
Space.IsDistBounded.const_smul
Project documentation
The boundedness condition on a function Space d → F for it to form a distribution. -/ @[fun_prop] def IsDistBounded {d : ℕ} (f : Space d → F) : Prop := AEStronglyMeasurable (fun x => f x) volume ∧ ∃ n, ∃ c : Fin n → ℝ, ∃ g : Fin n → Space d, ∃ p : Fin n → ℤ, (∀ i, 0 ≤ c i) ∧ (∀ i, - (d - 1 : ℕ) ≤ p i) ∧ ∀ x, ‖f x‖ ≤ ∑ i, c i * ‖x + g i‖ ^ p i namespace...
Exact Lean statement
@[fun_prop]
lemma const_smul {d : ℕ} [NormedSpace ℝ F] {f : Space d → F}
(hf : IsDistBounded f) (c : ℝ) : IsDistBounded (c • f)Formal artifact
Lean source
@[fun_prop]lemma const_smul {d : ℕ} [NormedSpace ℝ F] {f : Space d → F} (hf : IsDistBounded f) (c : ℝ) : IsDistBounded (c • f) := by rcases hf with ⟨hae1, ⟨n1, c1, g1, p1, c1_nonneg, p1_bound, bound1⟩⟩ refine ⟨by fun_prop, n1, ‖c‖ • c1, g1, p1, fun i => mul_nonneg (norm_nonneg c) (c1_nonneg i), p1_bound, fun x => ?_⟩ simp only [Pi.smul_apply, norm_smul, smul_eq_mul, mul_assoc, ← Finset.mul_sum] exact mul_le_mul_of_nonneg_left (bound1 x) (norm_nonneg c)- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/SpaceAndTime/Space/IsDistBounded.lean:555-562
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