Displaying similar documents to “The general Fubini theorem in complete bornological locally convex spaces.”

How subadditive are subadditive capacities?

George L. O'Brien, Wim Vervaat (1994)

Commentationes Mathematicae Universitatis Carolinae

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Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic...

A characterization of some additive arithmetical functions, III

Jean-Loup Mauclaire (1999)

Acta Arithmetica

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I. Introduction. In 1946, P. Erdős [2] proved that if a real-valued additive arithmetical function f satisfies the condition: f(n+1) - f(n) → 0, n → ∞, then there exists a constant C such that f(n) = C log n for all n in ℕ*. Later, I. Kátai [3,4] was led to conjecture that it was possible to determine additive arithmetical functions f and g satisfying the condition: there exist a real number l, a, c in ℕ*, and integers b, d such that f(an+b) - g(cn+d) → l, n → ∞. This problem...

Products of completion regular measures

David Fremlin, S. Grekas (1995)

Fundamenta Mathematicae

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We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.