the theory of dimensionally oriented sets; that is, an interpretation of surfaces as oriented boundaries of sets in space. Also in this paper, the family of sets approximable by polygonal domains of finite perimeter, known today as Caccioppoli sets or sets of finite perimeter, was introduced and studied. His last works, produced between 1952 and 1953, deal with a class of pseudoanalytic functions, introduced by him to extend certain properties of analytic functions. Legacy In 1992 his tormented personality inspired the plot of a film directed by Mario Martone, The Death of a Neapolitan Mathematician (Morte di un matematico napoletano), in which he was portrayed by Carlo Cecchi. An asteroid, 9934 Caccioppoli, has been named after him. Selected publications (Volume 1) AND (Volume 2). His "Selected works", a selection from Caccioppoli's scientific works with a biography and a commentary. See also Contraction principle Caccioppoli set Weyl's inequality References Biographical and general references This article is based largely on material from the equivalent article on Italian Wikipedia, accessed 4 March 2006, and also on the following biographical works: . the chapter on Caccioppoli in a book collecting brief biographical sketches and bibliographies of the scientific works produced by the mathematicians who taught at the Parthenope University of Naples during their stay. . The recollections on him by one of his colleagues and close friend. . An ample biographical paper on him written by Carlo Sbordone, pupil of Federico Cafifiero. . A brief obituary, basically announcing the commemoration of his scientific work published in the following issue 4 of the same Bulletin. . A survey on his research work published in the UMI Bulletin: even if no author is stated, attributes the article to Gianfranco Cimmino. References describing his scientific contributions . is the opening address of the 1988 academic year of the Società Nazionale di Scienze, Lettere ed Arti in Napoli: it describes the contributions of Caccioppoli, Miranda and Cafiero to real analysis and measure theory during their stay in Naples. (reviews of the symposium paper, see below). This paper, , is a reprint of the contribution of Paulo de Lucia from the "International Symposium Renato Caccioppoli" held in Napoli on 20–22 September 1989 and describes Caccioppoli's and Cafiero's contributions to the development of Measure Theory. The collection includes other papers detailing Caccioppoli's personality and his research, the introduction to his "Opere scelte" (Selected works), a conference held by Caccioppoli himself