Convergence near a point and the Arzela-Ascoli-type theorems
- 31 Downloads
Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are introduced locally; on a segment, they are equivalent to the quasiuniform convergence and to the uniform convergence of a sequence of functions, respectively.
Unable to display preview. Download preview PDF.
- 1.N. N. Luzin,Theory of Functions of a Real Variable [in Russian], Uchpedgiz, Moscow (1948).Google Scholar