Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.29 (1998) s.


Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Recent Submissions

Now showing 1 - 5 of 5
  • Publication
    Measures in Convex Geometry
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 1998)
    Schneider, Rolf
    By convex geometry we understand here the geometry of convex bodies in Euclidean space. In this field, measure theory enters naturally and is useful under several different aspects. First, like in many other fields, measures are employed to quantify the smallness of certain exceptional sets. In our first chapter, we give examples showing how Hausdorff measures of different dimensions are appropriate tools for describing sets of singular points or directions related to the boundary structure of convex bodies. In the second chapter we treat measures that are designed to refflect the local behaviour of convex bodies in a simi¬lar way as curvatures are used in differential geometry. The third connection between convex geometry and measure theory that we want to explain is of an entirely different nature. Here we treat a special class of convex bodies, the zonoids, which can be defined in terms of measures, and we show by an example from stochastic geometry how they are related to other fields. The second of these topics will be treated in greater detail than the other two. Naturally, some facts from the geometry of convex bodies will have to be used without proof. The fundamental notions will be explained and are easy to understand, due to their intuitive character. As a reference where proofs can be found, we mention the book [42].
      970  576
  • Publication
    Decomposition and Extension of Abstract Measures in Riesz Spaces
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 1998)
    Schmidt, Klaus D.
    The aim of these notes is to review some recent developments in the theory of abstract measures taking their values in Riesz space. The terni abstract measure is used were to denote a common abstraction of vector measures and linear operators. The topics considered in this survey are: A common approach to vector measures and linear operators, Jordan and Lebesgue decompositions of abstract measures and their applications to vector measures and linear operators, common extensions of linear operators and of vector measures, and extensions of modular functions. We also propose a number of open problems which may stimulate further research in this area. The material of these notes is based on the monograph by Schmidt [5l], two papers by Schmidt and Waldschaks [55], [56], and the PhD Thesis of Waldschaks [60].
      800  876
  • Publication
    On Additive Continuous Functions of Figures
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 1998)
    Pfeffer, W. F.
    This is an extended summary of results obtained previously by Z. Buczolich and the author [5]. It describes the relationship between derivatives and variational measures of additive continuous functions of figures, and presents a full descriptive definition of a generalized Riemann integral based on figures.
      1072  431
  • Publication
    Some important theorems in measure theory
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 1998)
    Bhaskara Rao, K. P. S.
    In this monograph I shall give several important theorems in measure theory which are not included in any regular graduate/undergraduate courses in measure theory nor are they normally included in standard text books in measure theory. All these theorems are important and have several applications. I shall assume that you know some set theory, some Boolean algebras and some functional analysis. You should definitely know some basic measure theory. Since my aim is to make you familiar with these theorems and their proofs I make no attempt to give the most general versions. Instead, I confine myself to the simplest possible versions without losing the beauty of the proofs.
      757  692
  • Publication
    The Invariant Subspace Problem: Some Recent Advances
    (Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 1998)
    Abramovich, Y. A.
    Burkinshaw, O.
    Aliprantis, C. D.
    This paper is devoted to recent developments regarding the invariant subspace problem for positive operators on Banach lattices. Some of this material was presented by Y. A. Abramovich at "Workshop di Teoria della Misura e Analisi Reale" Grado (Italia) 18-30 September 1995.
      1289  629