[3] **viXra:1308.0105 [pdf]**
*submitted on 2013-08-19 12:19:46*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 6 Pages.

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 some fundamental 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.

**Category:** Functions and Analysis

[2] **viXra:1308.0096 [pdf]**
*submitted on 2013-08-19 04:32:59*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 5 Pages.

We investigate the order of
approximation of a real-valued function
by means of suitable families of sampling type
operators, which include both discrete
and integral ones. We give a unified approach, by
means of which it is possible to consider several
kinds of classical operators, for instance Urysohn
integral operators, in particular Mellin-type
convolution integrals, and generalized sampling
series. We deal with filter convergence, and our results are proper extensions of the classical ones.

**Category:** Functions and Analysis

[1] **viXra:1308.0017 [pdf]**
*submitted on 2013-08-03 18:40:35*

**Authors:** Quentin Hampus Dawkings

**Comments:** 2 Pages.

We derive a formula for triple integrating trilinear forms.

**Category:** Functions and Analysis