Related papers: Almost uniform vs. pointwise convergence from a li…

In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…

In this paper, pointwise convergence, uniform convergence and compact convergence of sequences of holomorphic functions on an open subset of the complex plane are compared from a linear point of view. In fact, it is proved the existence of…

Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…

It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong…

It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…

The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…

Uniform metastable convergence is a weak form of uniform convergence for a family of sequences. In this paper we explore the way that metastable convergence stratifies into a family of notions indexed by countable ordinals. We give two…

In general, some of the well known results of measure theory dealing with the convergence of sequences of functions such as the Dominated Convergence Theorem or the Monotone Convergence Theorem are not true when we consider arbitrary nets…

Large algebraic structures are found inside the space of sequences of continuous functions on a compact interval having the property that, the series defined by each sequence converges absolutely and uniformly on the interval but the series…

In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in $[0,+\infty)$ and of the family of sequences of these functions converging to zero uniformly on compacta and in…

We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

We investigate a relations of almost isometric embedding and almost isometry between metric spaces and prove that with respect to these relations: (1) There is a countable universal metric space. (2) There may exist fewer than continuum…

We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat…

The paper contains two results pointing to the lack of symmetry between measure and category. Assume CH. There exists a strongly meager subset of the Cantor set that can be mapped onto the Cantor set by a uniformly continuous function. (It…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…

We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize…

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…