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On Some Properties of Vector Measures
Proceedings of the Steklov Institute of Mathematics, 2018Let \(E\) be a separable Banach space, \((T,\mathcal{T},\mu)\) a finite nonatomic measure space, \(S\) a separable metric space and \((p_n)_{n\in\mathbb{N}}\) a partition of unity subordinate to a locally finite cover \((V_n)_{n\in\mathbb{N}}\) of \(S\). For \(n\in\mathbb{N}\), let \(S\ni s\mapsto f_{n,s}\) be a continuous map into the space \(L^1(\mu ,
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Measurability Properties of Mazurkiewicz Sets
2022Summary: We consider the family of Mazurkiewicz subsets of the Euclidean plane from the measure-theoretical point of view. In particular, it is shown that all Mazurkiewicz sets are negligible and there exists a Mazurkiewicz set which is absolutely negligible.
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Differentiation Properties of Symmetric Measures
Potential Analysis, 2007Let the lower and upper derivative \(\underline D\mu(x)\) and \(\overline D\mu(x)\), respectively, of measures on the Lebesgue \(\sigma\)-algebra of \(\mathbb{R}^d\), \(d\in \mathbb{N}\), in a point \(x\in\mathbb{R}^d\) be defined with respect to cubes containing the point \(x\). Then the main result of the paper says, that for any symmetric measure on
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A Characteristic Property of Hausdorff Measure
Journal of the London Mathematical Society, 1950Man bezeichne mit \(h(x)\) eine für \(x\ge 0\) definierte, stetige, streng wachsende Funktion mit \(h(0) = 0\) und \(\displaystyle\varliminf_{x\to +0} h(\alpha x)/h(x) > 0\) \((0 < \alpha < 1)\). Ist ein separabler, metrischer Raum \(X\) gegeben, so definiert man für \(E\subset X\) \(\text{h. m. }E = \displaystyle\lim_{\delta\to 0} \Lambda_h(E, \delta)\
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Fundamentals of Measurement: Measurement: Knowledge from Information about Empirical Properties
IEEE Instrumentation and Measurement Magazine, 2023Luca Mari, Dario Petri
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Measurement of the physical properties of the snowpack
Reviews of Geophysics, 2015N J Kinar, John W Pomeroy
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