If $g$ is a function of real variable, define its quadratic variation over the interval $[0, t]$ as the limit (when it exits) $$[g](t) = \lim_{\delta_n \rightarrow 0}\sum_{i = 1}^n\left(g(t^n_i) - g(t^n_{i - 1})\right)^2,$$ where the limit is taken over partitions: $0 = t^n_0 < t^n_1 < \cdots < t^n_n = t$, with $\delta_n = \max_{1 \leq i \leq n} \left(t^n_i - t^n_{i - 1}\right)$.
Klebaner goes on to remark that this definition is not the same as $$\sup \sum_{i = 1}^n \left(g(t^n_i) - g(t^n_{i - 1})\right)^2$$ where supremum is taken over all partitions.