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The purpose of this note is to point out some corrections to the paper: A. Boccuto and X. Dimitriou, “Some new types of filter limit theorems for topological group-valued measures,” Real Anal. Exchange 39(1) (2014), 139-174.

Some Schur, Vitali-Hahn-Saks and Nikodým convergence theorems for \((l)\)-group-valued measures are given in the context of \((D)\)-convergence. We consider both the \(\sigma\)-additive and the finitely additive case. Here the notions of strong boundedness, countable additivity and absolute continuity are formulated not necessarily with respect to a same regulator, while the pointwise convergence of the measures is intended relatively to a common \((D)\)-sequence. Among the tools, we use the Fremlin lemma, which allows us to replace a countable family of \((D)\)-sequence with one regulator, and the Maeda-Ogasawara-Vulikh representation theorem for Archimedean lattice groups.

Here we present some comparison results between Birkhoff and McShane multivalued integration.

Some convergence theorems have been obtained for the $GH_k$ integral for functions defined in abstract topological spaces and with values in Riesz spaces.

The Ward and Perron integrals, with respect to abstract derivation bases, for Riesz-space-valued functions are introduced. It is shown that they are equivalent to the respectively defined Henstock-Kurzweil integral.

Some versions of Henstock-Kurzweil integral with respect to different derivation bases for functions with values in Dedekind complete Riesz spaces are studied. Fundamental Theorem of Calculus are proved for these integrals and an application to Walsh series is given.

Recently a connection has been found between the improper Kurzweil-Henstock integral on the real line and the integral over a compact space. In this paper these results are extended to a Pettis-type integral for the case of functions with values in Riesz spaces with ``enough" order continuous functionals.

Some versions of Dieudonné theorems are given for set functions, not necessarily positive, taking values in Dedekind complete $(l) $-groups, relatively to the "$(D)$-convergence"

Some new types of limit theorems for topological group-valued measures are proved in the context of lter convergence for suitable classes of lters. We investigate ( s)-boundedness, -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 lter 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. Mathematical Reviews subject classication

A monotone integral is given for scalar function, with respect to Riesz space values means, and also a necessary and sufficient condition to obtain a Radon-Nikodym density for two means.

Some Schur, Vitali-Hahn-Saks and Nikodým convergence theorems for (l)-group-valued measures are given in the context of (D)-convergence. We consider both the σ-additive and the finitely additive case. Here the notions of strong boundedness, countable additivity and absolute continuity are formulated not necessarily with respect to a same regulator, while the pointwise convergence of the measures is intended relatively to a common (D)-sequence. Among the tools, we use the Fremlin lemma, which allows us to replace a countable family of (D)-sequence with one regulator, and the Maeda-Ogasawara-Vulikh representation theorem for Archimedean lattice groups.

Some types of compactness in the ideal context are defined and relations between ideal exhaustiveness and equicontinuity of measures are investigated. As applications, some versions of limit theorems involving ideal pointwise convergence of measure sequences and some weak compactness results related to integral functionals are presented.

We find a decomposition of the type of Sobczyk-Hammer for measures with values in $l$-groups, and also deduce some convergence theorems for such decompositions. Our procedure is based on some theorems of the type of Vitali-Hahn-Saks, and on the so-called Stone extension method.

Some versions of Henstock-Kurzweil integral with respect to different derivation bases for functions with values in Dedekind complete Riesz spaces are studied. Fundamental Theorem of Calculus are proved for these integrals and an application to Walsh series is given.

Some versions of Dieudonn e theorems are given for set functions, not necessarily positive, taking values in Dedekind complete (l)-groups, relatively to the \(D)-convergence".