Arithmetic progressions of length three in subsets of a random set
Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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Lothar Redlin, Saleem Watson (1997)
Fundamenta Mathematicae
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Let X be a completely regular space and let A(X) be a ring of continuous real-valued functions on X which is closed under local bounded inversion. We show that the structure space of A(X) is homeomorphic to a quotient of the Stone-Čech compactification of X. We use this result to show that any realcompactification of X is homeomorphic to a subspace of the structure space of some ring of continuous functions A(X).
Valentin Gutev, Haruto Ohta (2000)
Fundamenta Mathematicae
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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
Rüdiger Göbel, R. Shortt (1994)
Fundamenta Mathematicae
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Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.
W. Jurkat, D. Nonnenmacher (1994)
Fundamenta Mathematicae
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We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.
Kurt Girstmair (1999)
Acta Arithmetica
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Peter J. Grabner, Pierre Liardet (1999)
Acta Arithmetica
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Mariusz Urbański (1996)
Fundamenta Mathematicae
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The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional packing measure is positive and finite. This latter measure can also be dynamically characterized...
Chaoping Xing, Harald Niederreiter (1995)
Acta Arithmetica
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