apply ContinuousOn.mul ?_ ?_ |>.aestronglyMeasurable (by simp)
N : ℕ
Npos : 0 < N
s : ℂ
s_re_gt : 0 < s.re
⊢ AEStronglyMeasurable (fun x => ↑x ^ (-s - 1) * ↑x.log) (volume.restrict (Ioi ↑N))
N : ℕ
Npos : 0 < N
s : ℂ
s_re_gt : 0 < s.re
⊢ ContinuousOn (fun x => ↑x ^ (-s - 1)) (Ioi ↑N)

N : ℕ
Npos : 0 < N
s : ℂ
s_re_gt : 0 < s.re
⊢ ContinuousOn (fun x => ↑x.log) (Ioi ↑N)