Definition:Lipschitz Space

Definition
Let $\struct {X _\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.

Let $\theta \in \openint 0 1$.

The space of Lipschitz mappings with respect to the metric $d_\theta$ is defined as:
 * $\ds\map {F_\theta} {X _\mathbf A} := \set { f \in \map C {X,\C} : \exists C\in\Z _{>0} \forall n\in\N : \map {\mathrm{var} _n} f \le C\theta ^n } $

where:
 * $\map C {X,\C}$ denotes the space of continuous mappings
 * $\mathrm {var}_n$ denotes the $n$th variation

Also see

 * Characterization of Lipschitz Continuity on Shift of Finite Type by Variations