Posts

Showing posts from December 29, 2018

If $X_nto X$ in $L^p$, is $E(X_n^p)to E(X^p)$ true?

Image
1 Let $p$ denote a positive integer. If $X_nto X$ in $L^p$ , is $E(X_n^p)to E(X^p)$ true? If each $X_n$ and $X$ are nonnegative, then it follows directly from Minkowski's inequality. Then how about the general case? I separated each $X_n$ into its positive and negative parts as $X_n=X_n^+-X_n^-$ , but it might not be the case that $X_n^+to X^+$ and $X_n^-to X^-$ in $L^p$ . probability-theory lp-spaces share | cite | improve this question edited Dec 2 at 12:42 Did 246k 23 220 454 asked Dec 2 at 11:37 ...