Dini's theorem

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What Wikipedia says

In the mathematical field of analysis, Dini's theorem says that if a monotone sequence of continuous functions converges pointwise on a compact space and if the limit function is also continuous, then the convergence is uniform. The theorem is named after Ulisse Dini.

Excerpt from the Wikipedia article “Dini's theorem”, under the CC BY-SA 4.0 license. Read the article on Wikipedia