English
The class yields a differentiable map when applied to ContDiffMap-supported functions.
Русский
Класс обеспечивает дифференцируемость для функций, поддерживаемых ContDiffMap.
LaTeX
$$$$\\text{ContDiff}(ℝ, n) f \\Rightarrow f\\text{ плавно дифференцируемый}.$$$$
Lean4
instance (B : Type*) (E F : outParam <| Type*) [NormedAddCommGroup E] [NormedAddCommGroup F] [NormedSpace ℝ E]
[NormedSpace ℝ F] (n : outParam ℕ∞) (K : outParam <| Compacts E) [ContDiffMapSupportedInClass B E F n K] :
BoundedContinuousMapClass B E F where
map_bounded
f := by
have := HasCompactSupport.intro K.isCompact (map_zero_on_compl f)
rcases (map_continuous f).bounded_above_of_compact_support this with ⟨C, hC⟩
exact map_bounded (BoundedContinuousFunction.ofNormedAddCommGroup f (map_continuous f) C hC)