Packing and doubling in metric spaces with curvature bounded above

We study locally compact, geodesically complete, CAT $$(\kappa )$$ spaces ( $$\hbox {GCBA}^\kappa $$ -spaces). prove a Croke-type local volume estimate only depending on the dimension of these spaces. show that doubling condition, with respect to natural measure, implies pure-dimensionality. Then we consider -spaces satisfying uniform packing condition at some fixed scale $$r_0$$ or arbitrarily small scale, and several compactness results pointed Gromov–Hausdorff convergence. Finally, as particular case, convergence stability $$M^\kappa -complexes bounded geometry.