English
If f and g are suitable, then the convolution integrand with swapped arguments is measurable: L(f(x−t), g(t)) is measurable as a function of t.
Русский
Если f и g удовлетворяют условиям, то интегранд свёртки со swapped аргументами измерим как функция t: L(f(x−t), g(t)).
LaTeX
$$AEStronglyMeasurable f μ → AEStronglyMeasurable g μ → AEStronglyMeasurable (λ t, L (f (x−t)) (g t)) μ$$
Lean4
theorem _root_.Continuous.convolution_integrand_fst [ContinuousSub G] (hg : Continuous g) (t : G) :
Continuous fun x => L (f t) (g (x - t)) :=
L.continuous₂.comp₂ continuous_const <| hg.comp <| continuous_id.sub continuous_const