# Arzelà-Ascoli theorem

From Encyclopedia of Mathematics

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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 |

#### Comments

#### References

[a1] | N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958) |

**How to Cite This Entry:**

Arzelà–Ascoli theorem.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Arzel%C3%A0%E2%80%93Ascoli_theorem&oldid=38676