We study the regularity properties of the lower and upper Hewitt–Stromberg outer measures on the \(\sigma \) -algebra of a complete separable metric space. We establish several structural properties of the lower Hewitt–Stromberg outer measure, showing in particular that it defines a metric outer measure. In contrast, we prove that the upper Hewitt–Stromberg outer measure is non-metric and thus fails to be a measure on the Borel \(\sigma \) -algebra. Under suitable conditions, we obtain new results on its inner regularity and clarify its behavior as a non-additive set function. These results contribute to a better understanding of the measure-theoretic and topological properties of Hewitt–Stromberg type constructions.
