Let $X$ be a Hausdorff topological space. A measure $\mu$ on the $\sigma$-algebra of Borel sets of $X$ is called a Radon measure if

1. i)

   for every $x\in X$ there exists an open neighbourhood $U$ of $X$ with $\mu(U)<\infty$,

2. ii)

   for every open set $U\subseteq X$ we have $\mu(U)=\sup\left\{\mu(K)\;\Big|\;K\subseteq U,\;K\text{ compact}\right\}$,

3. iii)

   for every Borel set $B$ of $X$ we have $\mu(B)=\inf\left\{\mu(U)\;\Big|\;B\subseteq U,\;U\text{ open}\right\}$.