Riesz-Markov-Kakutani Representation Theorem/Notation

Notation used
The purpose of this page is to document the notation used for the proof of the Riesz-Markov-Kakutani Representation Theorem.

For an open set $V \in \tau$ and a mapping $f \in \map {C_c} X$:


 * $f \prec V \iff \supp f \subset V$

where $\supp f$ denotes the support of $f$.

For a compact set $K \subset X$ and a mapping $f \in \map {C_c} X$:


 * $K \prec f \iff \forall x \in K: \map f x = 1$