I need a counterexample for the problem: If $r > s ≥ 1$, convergence in $s$-th mean does not imply convergence in $r$-th mean.

The definition for convergence in mean is as follows: Let $r≥1$ be a fixed number. A sequence of random variables $X_1, X_2, X_3,...$ converges in the $r$th mean to a random variable $X$, if

$$\lim_{n\to\infty}E(|X_n−X|^r)=0.$$

I need a counterexample for the problem: if $r>s\geq1$, convergence in $s^{\text{th}}$ mean does not imply convergence in $r^{\text{th}}$ mean.

The definition for convergence in mean is as follows: Let $r\geq1$ be a fixed number. A sequence of random variables $X_1, X_2, X_3,...$ converges in the $r^{\text{th}}$ mean to a random variable $X$, if

$$\lim_{n\to\infty}E(|X_n−X|^r)=0.$$

I need a counterexample for the problem: If $r > s ≥ 1$, convergence in $s$-th mean does not imply convergence in $r$-th mean.

The definition for convergence in mean is as follows: Let $r≥1$ be a fixed number. A sequence of random variables $X_1, X_2, X_3,...$ converges in the $r$th mean to a random variable $X$, if

$$\lim_{n\to\infty}E(|X_n−X|^r)=0$$.

I need a counterexample for the problem: If $r > s ≥ 1$, convergence in $s$-th mean does not imply convergence in $r$-th mean.

The definition for convergence in mean is as follows: Let $r≥1$ be a fixed number. A sequence of random variables $X_1, X_2, X_3,...$ converges in the $r$th mean to a random variable $X$, if

$$\lim_{n\to\infty}E(|X_n−X|^r)=0.$$

I need a counterexample for the problem: If r > s ≥ 1, convergence in s-th mean does not imply convergence in r-th mean

the definition for convergence in mean is as follows: Let r≥1 be a fixed number. A sequence of random variables X1, X2, X3, ⋯ converges in the rth mean to a random variable X, if

limn→∞$E(|Xn−X|^r)=0$.

I need a counterexample for the problem: If $r > s ≥ 1$, convergence in $s$-th mean does not imply convergence in $r$-th mean.

The definition for convergence in mean is as follows: Let $r≥1$ be a fixed number. A sequence of random variables $X_1, X_2, X_3,...$ converges in the $r$th mean to a random variable $X$, if

$$\lim_{n\to\infty}E(|X_n−X|^r)=0$$.