Definition 5.3.5A86EC2473CB6

Definition 5.3.5.A86EC2473CB6 Let $0\leq p\leq n$. A current $T$ of bidegree $(p,p)$ on $X$ is positive if $T(\varphi )\ge 0$ for every test form $\varphi $ of bidegree $(n-p,n-p)$ that is strongly positive at every point. We then write $T\geq 0$, and $T\geq S$ if $T-S\geq 0$. If $T$ is positive and $U$ is a coordinate chart, the trace measure of $T$ in $U$ is the positive Radon measure

where $\beta $ is the form (5.2.8) in the coordinates of $U$.