‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

Abstract We introduce a notion of sensitivity with respect to continuous real-valued bounded map which provides sufficient condition for transformation, acting on Baire metric space, exhibit generic subset points historic behavior (also known as irregular points). The applications this criterion recover, and extend, several theorems the genericity set, in addition yielding number new results, i...

One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natural to consider strengthenings of this statement in which one replaces countably many with א1-many. Even taking the compact space to be the unit interval, this already implies the failure of the Con...

Introduction. It is well known that a function which is a derivative is in the first Baire class, and it is also known that a function which is an approximate derivative is in the first Baire class. The analogous statement for partial derivatives of functions of more than one variable is of course not true. For if g is a nonmeasurable function of one variable, then the function f(x, y)=x-g(y) h...

The aim of this paper is to present a detailed explanation of three models of Shelah. We show the rule of the amalgamation in the construction of models in which all deenable sets of reals have Baire property or are Lebesgue measurable. Next we construct a model in which every projective set of reals has Baire property, a model with the Uniformization Property and a model of ZF + DC in which al...

It is shown that for each k > 1, if f is a Baire one function and f is the product of k bounded Darboux (quasi–continuous) functions, then f is the product of k bounded Darboux (quasi–continuous) Baire one functions as well.

We investigate the Baire category of I-convergent subsequences and rearrangements of a divergent sequence s = (sn) of reals, if I is an ideal on N having the Baire property. We also discuss the measure of the set of I-convergent subsequences for some classes of ideals on N. Our results generalize theorems due to H. Miller and C. Orhan (2001).

In this paper, we give alternative proofs of some of the properties of Baire-1 functions with respect to the new characterization of Baire-1 functions due to P.Y. Lee, W.K. Tang and D. Zhao. Some well-known functions were given to illustrate some of these properties. Mathematics Subject Classification: Primary 26A21