English
A reiteration that birkhoffAverage with respect to R equals birkhoffAverage with respect to S; a restatement of 113249/113250 in a taut form.
Русский
Повторение того, что среднее Биркхоффа не зависит от кольца – эквивалентность для разных колец.
LaTeX
$$$\mathrm{birkhoffAverage}(R,f,g,n,x) = \mathrm{birkhoffAverage}(S,f,g,n,x).$$$
Lean4
theorem birkhoffAverage_neg {f : α → α} {g : α → M} : birkhoffAverage R f (-g) = -birkhoffAverage R f g :=
by
funext _ x
simp [birkhoffAverage, birkhoffSum]