Definition:Horizontal Section of Function

Definition

Let $X$ and $Y$ be sets.

Let $f : X \times Y \to \overline \R$ be an extended real-valued function.

Let $y \in Y$.

We define the $y$-horizontal section $f^y$ of $f$ by:

$\map {f^y} x = \map f {x, y}$

for each $x \in X$.

Sources

• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $5.1$