In this paper n, k are natural numbers, X is a non empty set, and S is a σ-field of subsets of X. Next we state several propositions: (1) Let M be a σ-measure on S, F be a function from N into S, and given n. Then {x ∈ X: ∧ k (n ≤ k ⇒ x ∈ F (k))} is an element of S. (2) Let F be a sequence of subsets of X and n be an element of N. Then (the superior set sequence of F )(n) = ⋃ rng(F ↑ n) and (th...

" I think you might do something better with the time " , Alice said, " than wasting it in asking riddles that have no answer ... " Getting started First year undergraduates usually learn about the classical Rolle's theorem saying that between two consecutive zeros of a smooth function f one can always find at least one zero of its derivative f ′. In this paper we study a generalization of Roll...

In this article we prove a convergence S-arithmetic Khintchine-type theorem for product of non-degenerate ν-adic manifolds, where one of them is the Archimedian place.

In this note we introduce and study the new spectral properties (Bb), (Bab) and (Baw) as continuation of [7, 8, 12] which are variants of the classical Browder’s theorem.

the aim of this paper is to prove new quantitative uncertainty principle for the generalized fourier transform connected with a dunkl type operator on the real line. more precisely we prove an lp-lq-version of morgan's theorem.

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

In these notes we discuss Shannon’s noiseless coding theorem, which is one of the founding results of the field of information theory. Roughly speaking, we want to answer such questions as how much information is contained in some piece of data? One way to approach this question is to say that the data contains n bits of information (in average) if it can be coded by a binary sequence of length...

Robinson’s implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.

1 Dirichlet’s theorem — set up Dirichlet’s famous theorem from 1837 asserts that if k is a positive integer and a is an integer coprime to k, then there are infinitely many primes p with p ≡ a (mod k). In this unit we will prove the stronger assertion that the sum of the reciprocals of the primes p ≡ a (mod k) is divergent. Important in the proof is the use of the orthogonality relations for th...

1. Opening w HAT IS T H E EPISTEMOLOGICAL STATUS O F O U R KNOWledge of the truths of arithmetic? Are they analytic, the products of pure reason, as Leibniz held? O r are they high-level empirical truths that we know only a posteviori, as some empiricists, particularly Mill, have held? O r was Kant right to say that, although our lulowledge that '5+7=12' depends essentially upon intuition, it i...