I've never seen this notation before, and I'm having trouble finding a reference through search. Could someone explain what these notations mean for me?

In context, the statement they're in is the following:
a bounded $f$ is Riemann integrable iff
$$\varliminf\_{||C||\to 0}\mathcal{L}(f; C)\ge\varlimsup\_{||C||\to 0}\mathcal{U}(f;C)$$
where $C$ is a non-overlapping, finite, exact cover of a rectangular region $J$ in $\mathbb{R}^N$, $||C||$ denotes mesh size, and $\mathcal{L}, \mathcal{U}$ represent the lower and upper Riemann sums, respectively.