The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σadditive measure a ...

We show that any lattice of finite length is isomorphic to the lattice of fully dependent flats of a rank-finite independence space, which is finite if the given lattice is finite. If a suitable submodular function is given on the lattice, the independence space may be so chosen that this submodular function corresponds to the rank function of the independence space under the constructed isomor...

We propose an extension of a result by Repetowicz et al. (Repetowicz 2004) about Wick’s theorem and its applications: we first show that Wick’s theorem can be extended to the uniform distribution on the sphere and then to the whole class of elliptical distributions. Then, as a special case, we detail this result for distributions that are scale mixtures of Gaussians. Finally, we show that these...

It is a classical result (essentially due to Hölder) that if Γ is a subgroup of Homeo+(R) such that every nontrivial element acts freely then Γ is Abelian. A natural question to ask is what if every nontrivial element has at most N fixed points where N is a fixed natural number. In the case of N = 1, we do have a complete answer to this question: it has been proved independently by Solodov (not...

We extend an argument of Felix Behrend to show that fairly dense subsets of the integers exist which contain no solution to certain systems of linear equations.

Constructive meaning is given to the assertion that every finite Boolean algebra is an injective object in the category of distributive lattices. To this end, we employ Scott’s notion of entailment relation, in which context we describe Sikorski’s extension theorem for finite Boolean algebras and turn it into a syntactical conservation result. As a byproduct, we facilitate proofs of several rel...

The following extension of Dirac’s Theorem was conjectured by Enomoto, Kaneko and Tuza: if G is an n-vertex graph with minimum degree at least n/k, then there are k − 1 cycles in G covering the ∗Research is partially supported by Simons Fellowship, NSF CAREER Grant DMS0745185, Marie Curie FP7-PEOPLE-2012-IIF 327763. †Supported by grant no. 6910960 of the Fonds National de la Recherche, Luxembou...

We generalise an extension theorem for terraces for abelian groups to apply to nonabelian groups with a central subgroup isomorphic to the Klein 4-group V . We also give terraces for three of the non-abelian groups of order a multiple of 8 that have a cyclic subgroup of index 2 that may be used in the extension theorem. These results imply the existence of terraces for many groups that were not...

Let p be a prime. A famous theorem of Lucas states that (mp+s np+t ) ≡ (m n )(s t ) (mod p) if m,n, s, t are nonnegative integers with s, t < p. In this paper we aim to prove a similar result for generalized binomial coefficients defined in terms of second order recurrent sequences with initial values 0 and 1.

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull&apos;s intersection theorem of fuzzy ideals by using concept $mu$-adic...