Change of variables in a multiple integral for local fields
A proof of the formula \(\int_ U f\circ\varphi\;|\text{det }D_ \varphi|\;d\mu=\int_{\varphi(U)}f\;d\mu\) for locally compact fields \(\mathbb{K}\) and \(C^ 1\)-isomorphisms \(\varphi: U\to V\), where \(U\) and \(V\) are open subsets of \(\mathbb{K}^ n\), was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other.
scientific article; zbMATH DE number 164920