Let $m^n: \mathcal{L}^n \to [0,\infty]$ be the Lebesgue measure on $\mathbb{R}^n$, and let $\mathcal{B}^n$ denote the collection of Borel subsets of $\mathbb{R}^n$. Is there a name for the measure $m^n|_{\mathcal{B}^n}$? The terms "canonical" Borel measure or the "standard" Borel measure on $\mathbb{R}^n$ sound reasonable, but are either of them used in practice?
Also, is there a commonly used notation for $m^n|_{\mathcal{B}^n}$? I was thinking perhaps $\mu_b$ (provided that the dimension $n$ is understood from the context), though this conflicts slightly with the notation in Folland, where $\mu_F$ denotes the Borel measure induced by a right-continuous increasing function $F: \mathbb{R} \to \mathbb{R}$ in the case $n = 1$...It would be nice to come up with an unambiguous notation that isn't too clunky.