# 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.

#### References

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