add — Mathlib

English

If f and g are absolutely continuous on [a,b], then f+g is absolutely continuous on [a,b].

Русский

Если f и g абсолютно непрерывны на [a,b], то f+g абсолютно непрерывна на [a,b].

LaTeX

$$$ \text{AbsolutelyContinuousOnInterval}(f,a,b) \Rightarrow \text{AbsolutelyContinuousOnInterval} (f+g) a b $$$

Lean4

theorem add (hf : AbsolutelyContinuousOnInterval f a b) (hg : AbsolutelyContinuousOnInterval g a b) :
    AbsolutelyContinuousOnInterval (f + g) a b :=
  hf.fun_add hg

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