On the Glivenko-Cantelli Theorem for Weighted Empiricals Based on Independent Random Variables
On the Glivenko-Cantelli Theorem for Weighted Empiricals Based on Independent Random Variables
For $X_1, \cdots, X_n$ independent real valued random variables and for $\alpha \in \lbrack 0, 1 \rbrack$, let $F_j(x) = \alpha P\lbrack X_j < x \rbrack + (1 - \alpha)P\lbrack X_j \leqq x \rbrack$ and $Y_j(x) = \alpha I_{\lbrack X_j < x \rbrack} + (1 - \alpha) I_{\lbrack X_j \leqq …