Is there a name for the following asymmetry property of a measure on $R$?:

Question

Let $\mu$ be a Borel measure on $\mathbb{R}$. I am looking for a name for the following property: $\int_\mathbb{R} f d\mu \ge 0$ for all skew-symmetric Borel functions $f$ that are non-negative on $[0,\infty)$. This property is equivalent to $\mu(A) \ge \mu(-A)$ for any Borel subset of $[0,\infty)$, i.e. it expresses that the measure gives more weight to any set of positive numbers than to its mirror image.

Answer 1

Only thing that comes to mind is the is to say the measure is skewed so i guess you can say "skewed towards the right" or something like that.