I am reading "Analysis on Manifolds" by James R. Munkres.
If $A$ and $B$ are open sets in $\mathbb{R}^n$ and if $g:A\to B$ is a one-to-one function carrying $A$ onto $B$ such that both $g$ and $g^{-1}$ are of class $C^r$, then $g$ is called a diffeomorphism (of class $C^r$).
Theorem 17.2 (Change of variables theorem). Let $g:A\to B$ be a diffeomorphism of open sets in $\mathbb{R}^n$. Let $f:B\to\mathbb{R}$ be a continuous function. Then $f$ is integrable over $B$ if and only if the function $(f\circ g)|\det Dg|$ is integrable over $A$; in this case, $$\int_B f=\int_A (f\circ g)|\det Dg|.$$
In the statement of Theorem 17.2, $g$ is a diffeomorphism (of class $C^r$).
But the author didn't write the value of $r$.
What is the value of $r$?
Is $r$ equal to $1$?
I read Wikipedia about the change of variables theorem.
$r$ was $1$ in Wikipedia.