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Range of density measures

Martin Sleziak, Miloš Ziman (2009)

Acta Mathematica Universitatis Ostraviensis

We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence A ( n ) n as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...

Removability of singularities with anisotropic growth

Miroslav Dont, Josef, Jr. Král (2003)

Mathematica Bohemica

With help of suitable anisotropic Minkowski’s contents and Hausdorff measures some results are obtained concerning removability of singularities for solutions of partial differential equations with anisotropic growth in the vicinity of the singular set.

Semivariations of an additive function on a Boolean ring

Zbigniew Lipecki (2009)

Colloquium Mathematicae

With an additive function φ from a Boolean ring A into a normed space two positive functions on A, called semivariations of φ, are associated. We characterize those functions as submeasures with some additional properties in the general case as well as in the cases where φ is bounded or exhaustive.

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