Some Regular Properties of the Hewitt–Stromberg Measures with Respect to Doubling Gauges

The aim of this paper is to show that if the Hewitt–Stromberg pre-measures with respect to the gauge are finite, then these pre-measures have a kind of outer regularity in a general metric space X . We give also some conditions on the Hewitt–Stromberg pre-measures with respect to the gauge such that the Hewitt–Stromberg measures have an almost inner regularity on a complete separable metric space X .