ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D4248
Almost everywhere constant map
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
A D18: Map $f : X \to Y$ is almost everywhere constant with respect to $M$ if and only if \begin{equation} \exists \, y \in Y : \mu(f \neq y) = 0 \end{equation}
Formulation 1
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
A D18: Map $f : X \to Y$ is almost everywhere constant with respect to $M$ if and only if \begin{equation} \exists \, y \in Y : \mu(\{ x \in X : f(x) \neq y \}) = 0 \end{equation}
Subdefinitions
Constant map