Definition: For any real number \(r > 0\), \(\x_n\) converges in \(r\)th mean to \(\x\), denoted \(\x_n \overset{r}{\longrightarrow} \x\), if
\[\Ex\norm{\x_n-\x}^r \to 0.\]The most common case is \(r=2\), where it is called convergence in quadratic mean and denoted \(\x_n \inQM \x\).
See also: Proving consistency via quadratic mean