In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does not depend on x.
The concept is important because several properties of the functions fn, such as continuity and Riemann integrability, are transferred to the limit f if the convergence is uniform.
Uniform convergence to a function on a given interval can be defined in terms of the uniform norm.
Read more about Uniform Convergence: History, Definition, Examples, Properties, Almost Uniform Convergence
Famous quotes containing the word uniform:
“The maples
Stood uniform in buckets, and the steam
Of sap and snow rolled off the sugarhouse.”
—Robert Frost (1874–1963)