weak convergence

Suppose X is a topological vector spaceMathworldPlanetmath, X is the continuous dual of X, and x0,x1, is a sequence in X. Then we say that xi converges weakly to xX if


for every fX. The notation for this is xi𝑤x.

Title weak convergenceMathworldPlanetmath
Canonical name WeakConvergence
Date of creation 2013-03-22 15:00:58
Last modified on 2013-03-22 15:00:58
Owner matte (1858)
Last modified by matte (1858)
Numerical id 8
Author matte (1858)
Entry type Definition
Classification msc 46-00
Related topic WeakConvergenceInNormedLinearSpace
Related topic ConvergenceInDistribution