Approximation properties of measures generated by continuous set functions

Let X be a metric space and τ a non-negative function on the subsets of X. By the well-known Carathéodory process, we generate outer measures μδ(τ), for δ > 0, and (see §3). When, for every A ⊂ X, τA = (diamA)s for s ≥ 0, μ(τ) is the Hausdorff s-dimensional measure, and, if τA = h(diam A) for a m...

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Veröffentlicht in:	Mathematika 1962-12, Vol.9 (2), p.145-156
Hauptverfasser:	Sion, M., Sjerve, D.
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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