Arzelà-Ascoli theorem

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The name of a number of theorems that specify the conditions for the limit of a sequence of continuous functions to be a continuous function. One such condition is the quasi-uniform convergence of the sequence.


[1] C. Arzelà, Mem. Accad. Sci. Bologna (5) , 5 (1893) pp. 225–244
[2] G. Ascoli, Rend. Accad. Lincei , 18 (1883) pp. 521–586



[a1] N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958)
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Arzelà-Ascoli theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article