The Hausdorff metric and convergence in measure.
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چکیده
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the investigation of research articles in applied linguistics: convergence and divergence in iranian elt context
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Boundedness conditions of Hausdorff h-measure in metric spaces
The fractal dimensions are very important characteristics of the fractal sets. A problem which arises in the study of the fractal sets is the determination of their dimensions. The Hausdorff dimension of this type of sets is difficult to be determined, even if the Box dimensions can be computed. In this article we present some boundedness conditions on the Hausdorff h-measure of a set, using th...
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Here, instead of taking a σ-algebra as given and then defining a measure on this σ-algebra (namely, on the measurable sets), we take an outer measure as given and then define measurable sets using this outer measure. Carathéodory’s theorem states that the collection M of ν-measurable sets is a σ-algebra and that the restriction of ν to M is a complete measure. Suppose that (X, ρ) is a metric sp...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1974
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001209