uniform convergence of integral

Let the function  f(x,t)  be continuousMathworldPlanetmath in the domain


where b is a real number or , and let the improper integral

F(t):=abf(x,t)𝑑x=limub-auf(x,t)𝑑x (1)

be convergent (http://planetmath.org/ImproperIntegral) in every point t of the interval[c,d].  We say that the on the interval  [c,d],  if for each positive number ε there is a value xε[a,b]  such that


when  xεx<b.

Title uniform convergence of integral
Canonical name UniformConvergenceOfIntegral
Date of creation 2013-03-22 14:40:30
Last modified on 2013-03-22 14:40:30
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 13
Author pahio (2872)
Entry type Definition
Classification msc 26A42
Related topic SumFunctionOfSeries
Related topic ConvergenceOfIntegrals
Defines integral converging uniformly
Defines uniformly converging integral