It is shoun that each mapping which defined on product of space of finite sequences and arbitrary topological space and which is continuous on the first variable and Baire class $α$ on the second variable is Baire class $α + 1$ on joint variables.

[1] Rudin W. Lebesgue first theorem // Math. Analysis and applications, Part B. Edited by L.Nachbin. Adv. in Math. supplem. studies 7B. Academic Press. – 1981. – P.741–747.

[2] Sobchuk O.V. Differently continuous functions on the space of finite sequences. – Chernivtsi, 1993. – 5 p. – Dep. in the State Technical University of Ukraine, N1701–Uk93.

[3] Kalancha A.K., Maslyuchenko V.K. Beriev's classification of vector-valued differently continuous functions on products with a finitely measurable cofactor // Collection of scientific works of Kamianets-Podilskyi State Pedagogical University. Physics and mathematics series (mathematics). – Kamianets-Podilskyi: Kamianets-Podilskyi State Pedagogical University, Information and Publishing Department. - 1998. – Issue. 4. – P.43–46.

[4] Maslyuchenko V.K., Sobchuk O.V. Beriev classification and $σ$-metrization spaces // Mat. studii. – 1993. – Vol. 3. – P.95–102.

[5] Kalancha A.K., Maslyuchenko V.K. Lebesgue-Czech dimension and Beriev classification of vector-valued distinctly continuous mappings // Ukr. Mat. Journal (forthcoming).

[6] Kalancha A.K., Maslyuchenko V.K., Mykhailiuk V.V. Application of Dugundzhi's theorem to questions of Beriev classification of vector-valued mappings // Mat. Methods and Phys.-Mechanical Fields (forthcoming).