2017
Том 69
№ 7

Всі номери

Сходимость возле точки и теоремы типа Арцела - Асколи

Кузьмич В. И.

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Абстракт

Theorems that give necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function are proved. The notions of convergence near a point and equipotential convergence near a point are introduced. These notions are defined locally; on a segment, they are equivalent to quasiuniform and uniform convergence of a sequence of functions, respectively.

Англомовна версія (Springer): Ukrainian Mathematical Journal 45 (1993), no. 8, pp 1215-1220.

Зразок цитування: Кузьмич В. И. Сходимость возле точки и теоремы типа Арцела - Асколи // Укр. мат. журн. - 1993. - 45, № 8. - С. 1090–1095.

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