I have some trouble understanding complete sufficient statistics?
Let $T=\Sigma x_i$ be a sufficient statistic.
If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete sufficient statistic.
But what does this mean? I've seen examples of uniform and Bernoulli (page 6 http://amath.colorado.edu/courses/4520/2011fall/HandOuts/umvue.pdf), but it's not intuitive, I got more confused seeing the integration.
Could someone explain in a simple and intuitive way?