On systems of null sets
K. Bhaskara Rao, R. Shortt (1999)
Colloquium Mathematicae
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The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.
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K. Bhaskara Rao, R. Shortt (1999)
Colloquium Mathematicae
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The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.
Malyugin, S.A. (2001)
Sibirskij Matematicheskij Zhurnal
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L. Ramsey (1996)
Colloquium Mathematicae
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Szalay, I. (2002)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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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...
Sharma, R.K., Srivastava, J.B., Khan, Manju (2007)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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M. S. Audu, A. Afolabi, E. Apine (2006)
Kragujevac Journal of Mathematics
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Chekhlov, A.R. (2001)
Sibirskij Matematicheskij Zhurnal
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Boonpok, Chawalit (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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Kevin Hutchinson (1995)
Acta Arithmetica
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0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely...
Karol Pąk (2014)
Formalized Mathematics
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In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. ...
Zelenyuk, E.G., Protasov, I.V. (2001)
Sibirskij Matematicheskij Zhurnal
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Isaeva, O.V., Medvedev, N.Ya. (2000)
Siberian Mathematical Journal
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W. Comfort, F. Trigos-Arrieta, Ta-Sun Wu (1997)
Fundamenta Mathematicae
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