Home In memory of Paolo
Article
Licensed
Unlicensed Requires Authentication

In memory of Paolo

  • Antonio Cavaliere and Paola Cavaliere EMAIL logo
Published/Copyright: May 13, 2024
Become an author with De Gruyter Brill

Abstract

Paolo de Lucia passed away on March 18, 2022 in Nyon, Switzerland.

He was undoubtedly one of the most respected experts on Real Analysis and Measure Theory, but most of us miss him first of all as a scientific role model, colleague and fatherly friend.

Last year, some of his coauthors, students and friends attended the ‘Abstract Measure Theory and Applications: a symposium remembering Paolo de Lucia’s contributions’, held in Naples on March 30–31, 2023, and contributed orally with lectures and speeches in the section ‘Memories’.

For this reason, this year we wish to commemorate him by transcribing our two contributions and keeping them unchanged, albeit without the familiar context of the symposium, because unchanged is the sorrow for his loss and the weight of his absence for those who knew him.

So, despite an unbridgeable distance, we can imagine him blushing slightly, smiling and saying ironically “At last, for me even a jurist agrees to publish in a mathematics journal”.

Acknowledgement

We are deeply grateful to Anatolij Dvurečenskij for his warm welcome and valuable support for our project.

  1. Communicated by Anatolij Dvurečenskij

References

[1] Bhaskara Rao, K. P. S.—Bhaskara Rao, M.: Charges on Boolean algebras and almost discrete spaces, Mathematika 20 (1973), 214–223.Search in Google Scholar

[2] Cavaliere, P.—de Lucia, P.: Regularity and exhaustivity for finitely additive functions. The Dieudonné’s convergence theorem, Sci. Math. Jpn. 66 (2007), 313–323.Search in Google Scholar

[3] Cavaliere, P.—de Lucia, P.: The Cafiero criterion on a Boolean ring, Rend. Accad. Sci. Fis. Mat. Napoli 75 (2008), 1–5.Search in Google Scholar

[4] Cavaliere, P.—de Lucia, P.: On Brooks-Jewett, Vitali-Hahn-Saks and Nikodým convergence theorems for quasi-triangular functions, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 20 (2009), 387–396.Search in Google Scholar

[5] Cavaliere, P.—de Lucia, P.: Some new results in non-additive measure theory, Commun. Appl. Anal. 13 (2009), 535–545.Search in Google Scholar

[6] Cavaliere, P.—de Lucia, P.—De Simone, A.: On the absolute continuity of additive and non-additive functions, Funct. Approx. Comment. Math. 50 (2014), 181–190.Search in Google Scholar

[7] Cavaliere, P.—de Lucia, P.—De Simone, A.: Boundedness of nonadditive quantum measures, Anna. Rep. Math. Phys. 74 (2014), 371–378.Search in Google Scholar

[8] Cavaliere, P.—de Lucia, P.—De Simone, A.: Functions determining locally solid topological Riesz spaces continuously embedded in L0, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), 151–160.Search in Google Scholar

[9] Cavaliere, P.—de Lucia, P.—De Simone, A.—Ventriglia, F.: On the Lebesgue decomposition for non-additive functions, Positivity 18 (2014), 489–503.Search in Google Scholar

[10] Cavaliere, P.—de Lucia, P. —Ventriglia, F.: On Drewnowski lemma for non-additive functions and its consequences, Positivity 14 (2010), 1–16.Search in Google Scholar

[11] Cavaliere, P.—de Lucia, P.—Weber, H.: Approximation of finitely additive functions with values in topological groups, Z. Anal. Anwend. 32 (2013), 477–495.Search in Google Scholar

[12] Cavaliere, P.—Ventriglia, F.: On nonatomicity for non-additive functions, J. Math. Anal. Appl. 415 (2014), 358–372.Search in Google Scholar

[13] de Lucia, P.: Vito Volterra e gli inizi della biomatematica, Department of Mathematics and Applications ‘Federico II’ preprint, no. 2 (2009), 1–11.Search in Google Scholar

[14] Denneberg, D.: Non-additive Measure and Integral, Kluwer Academic Publishers Group, Dordrecht, 1994.Search in Google Scholar

[15] Drewnowski, L.: Topological rings of sets, continuous set functions, integration I, II, III, Bull. Acad. Polon. Sci. Sr. Sci. Math. Astronom. Phys. 20 (1972), 269–276, 277–286, 439–445.Search in Google Scholar

[16] Drewnowski, L.: On the continuity of certain non-additive set functions, Colloq. Math. 38 (1977/78), 243–253.Search in Google Scholar

[17] Dubois, D.—Prade, H.: Fuzzy Sets and Systems. Theory and Applications, Academic Press, New York-London, 1980.Search in Google Scholar

[18] Hewitt, E.—Ross, K. A.: Abstract Harmonic Analysis I. Graduate Studies in Mathematics, Vol. 29, American Mathematical Society, Berlin-Göttingen-Heidelberg: Springer-Verlag, 1963.Search in Google Scholar

[19] Husain, T.: Introduction to Topological Groups, W. B. Saunders Co., Philadelphia, Pa.-London, 1966.Search in Google Scholar

[20] Kampé de Fériet, J.—Forte, B.—Benvenuti, P.: Forme générale de l’opération de composition continue d’une information, C.R. Acad. Sci. Paris 269 (1969), 529–534.Search in Google Scholar

[21] Klimkin, V. M.—Sribnaya, T. A.: Convergence of a sequence of weakly regular set functions, Math. Notes 62 (1997), 87–92.Search in Google Scholar

[22] König, H.: The Lebesgue decomposition theorem for arbitrary contents, Positivity 10 (2006), 779–793.Search in Google Scholar

[23] Klimkin, V. M.—Svistula, M. G. : On the pointwise limit of vector charges with the Saks property, Math. Notes 74 (2003), 385–392.Search in Google Scholar

[24] Lipecki, Z.: A characterization of group-valued measures satisfying the countable chain condition, Colloq. Math. 31 (1974), 231–234.Search in Google Scholar

[25] Mitrea, D.—Mitrea, I.—Mitrea, M.—Ziadé, Z.: Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces, J. Funct. Anal. 262 (2012), 4766–4830.Search in Google Scholar

[26] Niculescu, C. P.: An overview of absolute continuity and its applications. In: Inequalities and Applications. International Series of Numerical Mathematics (C. Bandle, L. Losonczi, A. Gilányi, Z. Páles, M. Plum, eds.), vol. 157, Birkhäuser Verlag, Basel, 2008, pp. 201–214.Search in Google Scholar

[27] Pap, E.: Null-additive Set Functions, Kluwer Academic Publishers Group, Dordrecht, 1995.Search in Google Scholar

[28] Pap, E.: Applications of decomposable measures on nonlinear differential equations, Novi Sad J. Math. 31 (2001), 89–98.Search in Google Scholar

[29] Saeki, S.: The Vitali-Hahn-Saks theorem and measuroids, Proc. Amer. Math. Soc. 114 (1992), 775–782.Search in Google Scholar

[30] Traynor, T.: Absolute countinuity for group-valued measures, Canad. Math. Bull. 16 (1973), 577–579.Search in Google Scholar

[31] Ventriglia, F: Cafiero theorem for k-triangular functions on an orthomodular lattice, Rend. Acc. Sci. fis. Mat. Napoli 75 (2008), 45–52.Search in Google Scholar

[32] Wang, Z.—Klir, G. J.: Generalized Measure Theory, Springer Science + Business Media, New York, 2009.Search in Google Scholar

[33] Weber, H.: Compactness in spaces of group-valued contents, the Vitali-Hahn-Saks theorem and Nikodym’s boundedness theorem, Rocky Mountain J. Math. 16 (1986), 253–275.Search in Google Scholar

[34] Weber, H.: FN-Topologies and group-valued measures. In: Handbook of measure theory, vol. I, II (E. Pap, ed.), North-Holland, Amsterdam, 2002, pp. 703–743.Search in Google Scholar

[35] Weber, S.: ⊥-decomposable measures and integrals for Archimedean t-conorms ⊥, J. Math. Anal. Appl. 101 (1984), 114–138.Search in Google Scholar

[36] Weber, S.: Conditional measures and their applications to fuzzy sets, Fuzzy Sets and Systems 42 (1991), 73–85.Search in Google Scholar

Received: 2024-01-10
Accepted: 2024-01-10
Published Online: 2024-05-13
Published in Print: 2024-02-26

© 2024 Mathematical Institute Slovak Academy of Sciences

Downloaded on 23.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2024-0019/html
Scroll to top button