Theorem: first_fourier_aux1 (PrimeNumberTheoremAnd/Wiener.lean)

State before:
n✝ : ℕ
A a b c d u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hψ : Continuous ψ
x : ℝ
n : ℕ
⊢ Measurable fun u => ↑‖𝐞 (-(u * (1 / (2 * π) * (↑n / x).log))) • ψ u‖₊
Tactic:
refine Measurable.comp ?_ (by fun_prop) |>.smul (by fun_prop)
  |>.nnnorm |>.coe_nnreal_ennreal
State after:
n✝ : ℕ
A a b c d u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hψ : Continuous ψ
x : ℝ
n : ℕ
⊢ Measurable ⇑𝐞

State before:
n✝ : ℕ
A a b c d u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hψ : Continuous ψ
x : ℝ
n : ℕ
⊢ Measurable ⇑𝐞
Tactic:
exact Continuous.measurable Real.continuous_fourierChar
State after:
no goals

State before:
n✝ : ℕ
A a b c d u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hψ : Continuous ψ
x : ℝ
n : ℕ
⊢ Measurable fun u => -(u * (1 / (2 * π) * (↑n / x).log))
Tactic:
fun_prop
State after:
no goals

State before:
n✝ : ℕ
A a b c d u x✝ y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hψ : Continuous ψ
x : ℝ
n : ℕ
⊢ Measurable fun u => ψ u
Tactic:
fun_prop
State after:
no goals