Let $X$ be a locally convex Hausdorff space and $X'$ its dual space. By the Mackey-Arens theorem, there is a finest locally convex topology $\tau$ on $Y$ such that $(Y, \tau)' = X$. $\tau$ is called the Mackey topology and it can be charaterized as the topology of uniform convergence on weakly compact convex balanced subsets of $X$.
In some literature, the authors sometimes refer to the topology of uniform convergence on weakly compact convex sets as the Mackey topology --- just google for "uniform convergence on weakly compact convex" "mackey".
Are these topologies really equal or are the authors just a little bit sloppy?
Edit: I think, the equality of these two topologies is at least true if $X$ is weakly complete since then the weak closure of the convex balanced hull of a weakly compact set remains weakly compact. For a general locally convex space the convex balanced hull of a compact set is only precompact and the closure need not be compact.