Definition 1.6.5.label Let $f: \bracs{k/n|k \in \nat_0}\to \real$, then the function
\[L_{n}f: \real_{\ge 0}\to \real \quad t \mapsto (1 - nr_{n}(t))f(\fl{t}_{n}) + nr_{n}(t)f(\fl{t}_{n} + n^{-1})\]
is the $n$-adic linearisation of $f$.
Definition 1.6.5.label Let $f: \bracs{k/n|k \in \nat_0}\to \real$, then the function
is the $n$-adic linearisation of $f$.