An D4767: Unsigned real number $C \in [0, \infty)$ is a

**Lipschitz constant**for $f$ with respect to $M_X$ and $M_Y$ if and only if \begin{equation} \forall \, x, y \in X : d_Y ( f(x), f(y)) \leq C d_X(x, y) \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Lipschitz map

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Lipschitz map

Formulation 0

Let $M_X = (X, d_X)$ and $M_Y = (Y, d_Y)$ each be a D1107: Metric space.

An D4767: Unsigned real number $C \in [0, \infty)$ is a**Lipschitz constant** for $f$ with respect to $M_X$ and $M_Y$ if and only if
\begin{equation}
\forall \, x, y \in X : d_Y ( f(x), f(y)) \leq C d_X(x, y)
\end{equation}

An D4767: Unsigned real number $C \in [0, \infty)$ is a

Child definitions