Geodesic
Equivalent definitions for the measurability of a multivariate function and Filippov's lemma
Mathematica Applicanda, Tome 7 (1979) no. 14, pp. 63-70.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

From the text: "In the many papers in which the concept of measurability of a multivariate function arises, the authors usually formulate one definition of measurability and ignore its connections with other definitions. Assuming that the space, in which the values of the multivariate function lie, which admits only a closed set, is metric and compact we prove that all well-known definitions of measurability of multivariate functions are equivalent. "A. F. Filippov's lemma was first formulated in 1959 [Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959, no. 2, 25–32; MR0122650] and was later generalized by many others, in particular by W. Furakawa [Ann. Math. Statist. 43 (1972), 1612–1622; MR0371418], C. J. Himmelberg [Fund. Math. 87 (1975), 53–72; MR0367142] and C. Olech [Bull. Acad. Polon Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 317–321; MR0199338]. Using various definitions of measurability of a multivariate function (whose equivalence we prove beforehand) we introduce two theorems on the existence of a measurable implicit function. These theorems generalize Furakawa's theorem [op. cit.] which is a reformulation of Olech's theorem [op. cit.] for Borel measurability.''
DOI : 10.14708/ma.v7i14.1431
Classification : 28A20
Mots-clés : Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 
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Adam Idzik. Equivalent definitions for the measurability of a multivariate function and Filippov's lemma. Mathematica Applicanda, Tome 7 (1979) no. 14, pp.  63-70. doi : 10.14708/ma.v7i14.1431. http://geodesic.mathdoc.fr/articles/10.14708/ma.v7i14.1431/

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