Definition:Homogeneous Function/Real Space/Zero Degree

Definition

Let $f: \R^2 \to \R$ be a real-valued function of two variables.

$\map f {x, y}$ is a homogeneous function of degree zero or of zero degree if and only if:

$\forall t \in \R: \map f {t x, t y} = t^0 \map f {x, y} = \map f {x, y}$