منابع مشابه
Weakly partitive families on infinite sets
Given a finite or infinite set S and a positive integer k, a binary structure B of base S and of rank k is a function (S × S) \ {(x, x) : x ∈ S} −→ {0, . . . , k− 1}. A subset X of S is an interval of B if for a, b ∈ X and x ∈ S \X, B(a, x) = B(b, x) and B(x, a) = B(x, b). The family of intervals of B satisfies the following: ∅, B and {x}, where x ∈ B, are intervals of B; for every family F of ...
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The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...
متن کاملOn Families of Weakly Cross-intersecting Set-pairs
Let F be a family of pairs of sets. We call it an (a, b)-set system if for every set-pair (A,B) in F we have that |A| = a, |B| = b, A ∩ B = ∅. The following classical result on families of cross-intersecting set-pairs is due to Bollobás [6]. Let F be an (a, b)-set system with the cross-intersecting property, i.e., for (Ai, Bi), (Aj, Bj) ∈ F with i 6= j we have that both Ai ∩ Bj and Aj ∩ Bi are ...
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We study the proof strength of various second order logic principles that make statements about families of sets and functions. Usually, families of sets or functions are represented in a uniform way by a single object. In order to be able to go beyond the limitations imposed by this approach, we introduce the concept of weakly represented families of sets and functions. This allows us to study...
متن کاملInfinite families of tight regular tournaments
In this paper, we construct infinite families of tight regular tournaments. In particular, we prove that two classes of regular tournaments, tame molds and ample tournaments are tight. We exhibit an infinite family of 3-dichromatic tight tournaments. With this family we positively answer to one case of a conjecture posed by V. Neumann-Lara. Finally, we show that any tournament with a tight mold...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2012
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2012-017-8