5 июн. 2016 г. · Dini's theorem states that monotone convergence of continuous functions on a compact set is uniform, provided the limit is continuous. When does pointwise convergence imply uniform convergence? Does pointwise convergence to a continuous function in ... Uniform convergence of a sequence of continuous functions on ... From pointwise to uniform convergence on compact sets Другие результаты с сайта math.stackexchange.com

In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence.

19 апр. 2020 г. · Pointwise convergence of any sequence of functions on a compact set implies uniform convergence.

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.

11 июл. 2024 г. · Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set? Certainly ...

First, in Euclidean space, a subset K is compact if and only if every sequence in K has a subsequence that converges in K. This is essentially the Bolzano– ...

24 нояб. 2023 г. · Final answer: Yes, pointwise convergence of continuous functions on a compact set to a continuous limit implies uniform convergence on that set.

Продолжительность: 8:04
Опубликовано: 31 мая 2019 г.

It can be easily verified that the sets S(x, U) form subbasis for some topology on Y X, which is called the topology of pointwise convergence.

The result proved below concerns a convex set of functions, measurable with respect to a fixed measure, and compact in the topology of pointwise convergence.