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.
Best Answer
It's definitely liminf and limsup. Maybe this notation is more common in Europe than in America? For example, the German Wikipedia page mentions it as an alternative. A well-known book that uses this notation is Hörmander's The Analysis of Linear Partial Differential Operators.