Scheffé’s theorem

Let X,X1,X2, be continuous random variables in a probability spaceMathworldPlanetmath, whose probability density functionsMathworldPlanetmath are f,f1,f2,, respectively. If fnf almost everywhere (relative to Lebesgue measureMathworldPlanetmath,) then Xn converges to X in distribution ( Xn𝐷X.

Title Scheffé’s theorem
Canonical name ScheffesTheorem
Date of creation 2013-03-22 13:14:23
Last modified on 2013-03-22 13:14:23
Owner Koro (127)
Last modified by Koro (127)
Numerical id 6
Author Koro (127)
Entry type Theorem
Classification msc 60E05