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Federico Cafiero
Federico Cafiero (24 May 1914 – 7 May 1980) was an Italian mathematician known for his contributions in real analysis, measure and integration theory, and in the theory of ordinary differential equations. In particular, generalizing the Vitali convergence theorem, the Fichera convergence theorem and previous results of Vladimir Mikhailovich Dubrovskii, he proved a necessary and sufficient condition for the passage to the limit under the sign of integral:〔See , and .〕 this result is, in some sense, definitive.〔According to .〕 In the field of ordinary differential equation, he studied existence and uniqueness problems under very general hypotheses for the left member of the given first order equation, developing an important approximation method and proving a fundamental uniqueness theorem.〔According to , who describes briefly these results, and to , who comprehensively present Cafiero's and other's research results in this field.〕
==Life and academic career==
Cafiero was born in Riposto, Province of Catania, on May 24, 1914.〔See and : his parents were from Meta di Sorrento, according to Miranda.〕 He obtained his Laurea in mathematics, cum laude, from the University of Naples Federico II in 1939.〔See .〕 During the 1939–1940 academic year, he won an "Istituto Nazionale di Alta Matematica" scholarship and went in Rome to the institute:〔See , and : Letta and Roghi clearly state the academic year, while Miranda states that he won the scholarship "''subito dopo''" i.e. "''soon after''" earning his Laurea degree. Roghi gives many other details about the scholarship, including the names of other winners and its amount, which was 5000 Italian liras.〕 there he followed the courses held by Francesco Severi, Mauro Picone, Luigi Fantappiè, Giulio Krall and Leonida Tonelli.〔 lists only the first four names while also mentions Tonelli but not Krall. gives the full list of the courses held at the institute during the 1939–1940 academic year, including the names of the appointed teachers: along the ones cited by Letta and Miranda, Enrico Bompiani, Giovanni Giorgi, Ugo Amaldi, Antonio Signorini and Fabio Conforto are also mentioned.〕
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