A generalization of the rogosinski-rogosinski theorem

• Date: 2000
• Main Authors: Dekanov, S. Ya., Mikhalin, G. A., Деканов, С. Я., Михалін, Г. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4410
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish necessary and sufficient conditions for numerical functions αj(x), j ∈ N, x ∈ X, under which the conditions K(f j ⊂ K(f 1) ∀j≥2 and \(\mathop {\lim }\limits_{U_r } \sum\nolimits_{j = 1}^\infty {\alpha _j (x)f_j (x) = a} \) yield \(\mathop {\lim }\limits_{U_r } f_1 (x) = a.\) T...