Definition:Lipschitz Norm

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

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

Let $\map {F_\theta} {X _\mathbf A}$ be the space of Lipschitz mappings.

The norm $\norm {\,\cdot\,} _\theta$ on $\map {F_\theta} {X _\mathbf A}$ is defined as:
 * $\ds \norm {\,\cdot\,}_\theta := \size {\,\cdot\,}_\infty + \size {\,\cdot\,}_\theta$

where:
 * $\size {\,\cdot\,}_\infty$ denotes the supremum norm
 * $\size {\,\cdot\,}_\theta$ denotes the Lipschitz seminorm.