The present writer's father,
W. H. Young, used to recall that this very question — what principle can we use as the foundation of the calculus of variations[4] — had been put him by a young Italian mathematician. His reply was a question: "Can you use semicontinuity?" The young Italian was Leonida Tonelli. Semicontinuity was then still a recent concept, known only to a few. In the hands of Tonelli, it became an important tool in a fundamental new approach to the calculus of variations.
Accademia Nazionale dei Lincei (2012),
Annuario dell'Accademia Nazionale dei Lincei 2012 – CDX dalla Sua Fondazione(PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734, archived from
the original(PDF) on 2016-03-04, retrieved 2016-05-15. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities.
Fichera, Gaetano (1995), "Tre battaglie perdute da tre grandi matematici italiani", Atti del convegno di studi in memoria di Giuseppe Gemignani. Modena, 20 maggio 1994, Collana di Studi dell'Accademia (in Italian), vol. 11,
Modena:
Enrico Mucchi Editore on behalf of the
Accademia Nazionale di Scienze, Lettere e Arti di Modena, pp. 9–28,
MR1385469{{
citation}}: External link in |publisher= (
help). This paper, included in the Proceedings of the Study Meeting in Memory of Giuseppe Gemignani, is an account of the failures of
Vito Volterra, Leonida Tonelli and
Francesco Severi, when dealing with particular research problems during their career. An English translation of the title reads as:-"Three battles lost by three great Italian mathematicians".
Cafiero, Federico (1959), Misura e integrazione, Monografie matematiche del
Consiglio Nazionale delle Ricerche (in Italian), vol. 5,
Roma: Edizioni Cremonese, pp. VII+451,
MR0215954,
Zbl0171.01503. Measure and integration (as the English translation of the title reads) is a definitive monograph on integration and measure theory: the treatment of the limiting behavior of the integral of various kind of
sequences of measure-related structures (measurable functions,
measurable sets, measures and their combinations) is somewhat conclusive.
The present writer's father,
W. H. Young, used to recall that this very question — what principle can we use as the foundation of the calculus of variations[4] — had been put him by a young Italian mathematician. His reply was a question: "Can you use semicontinuity?" The young Italian was Leonida Tonelli. Semicontinuity was then still a recent concept, known only to a few. In the hands of Tonelli, it became an important tool in a fundamental new approach to the calculus of variations.
Accademia Nazionale dei Lincei (2012),
Annuario dell'Accademia Nazionale dei Lincei 2012 – CDX dalla Sua Fondazione(PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734, archived from
the original(PDF) on 2016-03-04, retrieved 2016-05-15. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities.
Fichera, Gaetano (1995), "Tre battaglie perdute da tre grandi matematici italiani", Atti del convegno di studi in memoria di Giuseppe Gemignani. Modena, 20 maggio 1994, Collana di Studi dell'Accademia (in Italian), vol. 11,
Modena:
Enrico Mucchi Editore on behalf of the
Accademia Nazionale di Scienze, Lettere e Arti di Modena, pp. 9–28,
MR1385469{{
citation}}: External link in |publisher= (
help). This paper, included in the Proceedings of the Study Meeting in Memory of Giuseppe Gemignani, is an account of the failures of
Vito Volterra, Leonida Tonelli and
Francesco Severi, when dealing with particular research problems during their career. An English translation of the title reads as:-"Three battles lost by three great Italian mathematicians".
Cafiero, Federico (1959), Misura e integrazione, Monografie matematiche del
Consiglio Nazionale delle Ricerche (in Italian), vol. 5,
Roma: Edizioni Cremonese, pp. VII+451,
MR0215954,
Zbl0171.01503. Measure and integration (as the English translation of the title reads) is a definitive monograph on integration and measure theory: the treatment of the limiting behavior of the integral of various kind of
sequences of measure-related structures (measurable functions,
measurable sets, measures and their combinations) is somewhat conclusive.