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We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation. [ABSTRACT FROM AUTHOR]

In the present paper, we extend Gamidov's integral inequalities to time scales. The obtained results can be used as tools in the study of certain properties of dynamical equations on time scales. [ABSTRACT FROM AUTHOR]

We define and study, for subsets of [0;∞); several types of strong right upper porosity at the point 0. Some characterizations of these types of porosity are obtained, including a characterization in terms of a universal property and a characterization in terms of a structural property. [ABSTRACT FROM AUTHOR]

In this paper we investigate for which closed subsets P of the real line R there exists a continuous map from P onto P² and, if such a function exists, how smooth can it be. We show that there exists an infinitely many times differentiable function f:R → R² which maps an unbounded perfect set P onto P². At the same time, no continuously differentiable function f:R → R² can map a compact perfect set onto its square. Finally, we show that a disconnected compact perfect set P admits a continuous function from P onto P² if, and only if, P has uncountably many connected components. [ABSTRACT FROM AUTHOR]

Some new types of limit theorems for topological group-valued measures are proved in the context of filter convergence for suitable classes of filters. We investigate (s)-boundedness, σ-additivity and regularity properties of topological group-valued measures. We consider also Schur-type theorems, using the sliding hump technique, and prove some convergence theorems in the particular case of positive measures. We deal with the notion of uniform filter exhaustiveness, by means of which we prove some theorems on existence of the limit measure, some other kinds of limit theorems and their equivalence, using known results on existence of countably additive restrictions of strongly bounded measures. Furthermore we pose some open problems. [ABSTRACT FROM AUTHOR]

A weak selection on an infinite set X is a function f : [X]² → X such that f(F) ∈ F for each F ∈ [X]² := {E ⊆ X : |E| = 2}. If f : [X]² → X is a weak selection and x; y ∈ R, then we say that x

The purpose of this article is to give a solution to a problem raised by A. Maliszewski in [5] by showing that any lower semicontinuous function can be represented as a sum of two lower semicontinuous strong Šwiątkowski functions. [ABSTRACT FROM AUTHOR]

We investigate differences between upper and lower porosity. In finite dimensional Banach spaces every upper porous set is directionally upper porous. We show the situation is very different for lower porous sets; there exists a lower porous set in R² which is not even a countable union of directionally lower porous sets. [ABSTRACT FROM AUTHOR]

Here we present some comparison results between Birkhoff and Mc-Shane multivalued integration. [ABSTRACT FROM AUTHOR]

We prove that the Hausdorff dimension of the graph of a prevalent real-valued continuous function on the unit interval is 2. We also indicate how our results can be extended to the space of continuous functions on [0; 1]d for d ∈ ℕ and use this to obtain results on the 'horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of the graph of a generic continuous function. [ABSTRACT FROM AUTHOR]

The article offers information on the journal "Real Analysis Exchange," including a new section entitled "Plenary Lectures," its contributors, and publisher.

The article presents editorial messages for the 2014/2015 issue of "Real Analysis Exchange" including the help of Dr. Tatiana Sworowska with increasing demands for online content and the key roles of assistant editors Benjamin Bruce and Jennifer Crawford for the Summer Symposium in Real Analysis.