Ascoli's theorem

[as′kō‚lēz ‚thir·əm]

(mathematics)

The theorem that a set of uniformly bounded, equicontinuous, real-valued functions on a closed set of a real Euclidean n-dimensional space contains a sequence of functions which converges uniformly on compact subsets.

References in periodicals archive ?

Finally, combining Claim 1 to Claim 4 with Ascoli's theorem, we conclude that the operator [P.

Controllability of impulsive fractional differential equations with infinite delay

Therefore by Ascoli's theorem, the family {[[integral].

Positive bounded solutions for semilinear elliptic equations in smooth domains

He covers real numbers and limits, including the concepts of infinity and sequences, topology, including the Cantor set and fractals, and then progresses to calculus, including the Riemann integral, sequences of functions, power and Fourier series and the exponential function, closing with metric spaces, including Ascoli's theorem.