Papers by Benedetto Bongiorno
The school and university education of G.B. Guccia are presented. He studied in the new education... more The school and university education of G.B. Guccia are presented. He studied in the new educational system created when the Kingdom of Italy was founded. Sicily had a long story of cultivators of mathematics, which we briefly review. Shortly after G.B. Guccia entered university the most important encounter of his life occurred: he met the geometer Luigi Cremona and moved to Rome. Five years later he presented his thesis under the guidance of Cremona.
We review three important processes: the foundation of national mathematical societies, in partic... more We review three important processes: the foundation of national mathematical societies, in particular, the London Mathematical Society and the Societe Mathematique de France; the creation of research mathematical journals, focusing on Acta Mathematica and its founder Gosta Mittag-Leffler; and the organization of mathematics at international level, discussing the origins of the International Congresses of Mathematicians.
It is proved that the absolute continuity of the variational measure generated by an additive int... more It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.
Rendiconti del Circolo Matematico di Palermo, 1979
Page 1. RFNDICONTI DEL CIRCOLO MATEMATICO DI PALERMO &:fie II, Tomo XXVIII (1979), pp. 33-36 ... more Page 1. RFNDICONTI DEL CIRCOLO MATEMATICO DI PALERMO &:fie II, Tomo XXVIII (1979), pp. 33-36 ... Vale il seguente TEOREMA 1. Se Q3 gode della propriet?t /orte di Vitali, 0<p< + oo, e se (X--At)=0, allora: (2) fa IIF' (x)ll~ d~(x)= inf Vp (F, ~). (3) Dimostrazione. ...
The founding of the Circolo Matematico di Palermo and its journal, the Rendiconti del Circolo Mat... more The founding of the Circolo Matematico di Palermo and its journal, the Rendiconti del Circolo Matematico di Palermo are discussed. In order to understand the path that led to these two events, we follow G.B. Guccia’s post-doctoral journey in the summer of 1880 through Paris, Reims and London. Despite many initial difficulties, the early success of the society and the journal encouraged G.B. Guccia to lead the society towards internationalization.
G.B. Guccia had an ambitious goal: developing the Circolo Matematico di Palermo into the internat... more G.B. Guccia had an ambitious goal: developing the Circolo Matematico di Palermo into the international association of mathematicians. The pursuit of this aim was influenced by his two most important mathematical relationships: with Vito Volterra and with Henri Poincare. The time came to obtain a professorship, and to consolidate the Circolo Matematico di Palermo. On both issues, G.B. Guccia succeeded, although through rather turbulent processes. The celebration of the Heidelberg International Congress of 1904 was a fundamental moment for the international expansion of the Circolo Matematico di Palermo. The Rome International Congress of 1908 gave G.B. Guccia the opportunity to realize his ambitious goal.
We prove that the \(n\)-dimensional Perron integral with respect to the full interval basis, with... more We prove that the \(n\)-dimensional Perron integral with respect to the full interval basis, without any regularity condition, defined by continuous major and minor functions is equivalent to the one defined by major and minor functions which are not supposed to be continuous.
Real Analysis Exchange
It is proved that the absolute continuity of the variational measure generated by an additive int... more It is proved that the absolute continuity of the variational measure generated by an additive interval function F implies the differentiability almost everywhere of the function F and gives a full descriptive characterization of the Denjoy-Perron integral.
Real Analysis Exchange
We prove that the n-dimensional Perron integral with respect to the full interval basis, without ... more We prove that the n-dimensional Perron integral with respect to the full interval basis, without any regularity condition, defined by continuous major and minor functions is equivalent to the one defined by major and minor functions which are not supposed to be continuous.
Real Analysis Exchange
[2] to the case of an arbitrary σ-finite outer regular quasi-Radon measure space. We present an a... more [2] to the case of an arbitrary σ-finite outer regular quasi-Radon measure space. We present an alternate approach to the Fremlin integral for a non-atomic, finite quasi-Radon space.
Real Analysis Exchange
We introduce an n-dimensional Perron integral defined in terms of ordinary (in the Saks terminolo... more We introduce an n-dimensional Perron integral defined in terms of ordinary (in the Saks terminology) derivates. We prove that we get an equivalent definition of this integral if in the definition we use only continuous major and minor functions. We also prove that this integral is equivalent to a version of the Kurzweil-Henstock integral defined by Mawhin.
Illinois Journal of Mathematics
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Papers by Benedetto Bongiorno