We explore the relation between two 'rationality conditions' for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is...

We derived the Kuhn-Tucker theorem by assuming regularity of the binding constraints. With the possibility of corner solutions, regularity is too stringent. The regularity condition will not necessarily apply throughout the constraint set. Verifying the regularity condition requires knowing the optimal solution, but the first-order conditions will not identify the optimal solution unless the re...

For a word S, let f(S) be the largest integer m such that there are two disjoint identical (scattered) subwords of length m. Let f(n,Σ) = min{f(S) : S is of length n, over alphabet Σ}. Here, it is shown that 2f(n, {0, 1}) = n− o(n) using the regularity lemma for words. In other words, any binary word of length n can be split into two identical subwords (referred to as twins) and, perhaps, a rem...

Szemerédi’s Regularity Lemma is a well-known and powerful tool in modern graph theory. This result led to a number of interesting applications, particularly in extremal graph theory. A regularity lemma for 3-uniform hypergraphs developed by Frankl and Rödl [8] allows some of the Szemerédi Regularity Lemma graph applications to be extended to hypergraphs. An important development regarding Szeme...

Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

A. Regularity Conditions Within the text we have referred to regularity conditions on the MDP: Regularity conditions A.1: p(s′|s, a), ∇ap(s|s, a), μθ(s), ∇θμθ(s), r(s, a), ∇ar(s, a), p1(s) are continuous in all parameters and variables s, a, s′ and x. Regularity conditions A.2: there exists a b and L such that sups p1(s) < b, supa,s,s′ p(s′|s, a) < b, supa,s r(s, a) < b, supa,s,s′ ||∇ap(s|s, a)...

The closedness type regularity conditions have proven during the last decade to be viable alternatives to their more restrictive interiority type counterparts, in both convex optimization and different areas where it was successfully applied. In this review article we deand reconstruct some closedness type regularity conditions formulated by means of epigraphs and subdifferentials, respectively...