Question from Folland, criteron for a function to belong to $L^p$ This question is from Folland 6.38,
Show that $f \in L^p $ iff $\sum_{k=-\infty}^ {\infty} 2^{pk} \mu \{{x: |f(x)|>2^{k}}\} \lt \infty$


*

*If $f \in L^p $, I applied the Chebyshev's inequality 

*But for the other direction, I don't know how to begin.


Any advice would be appreciated.
Thanks

Note that 
$$\int|f|^pd\mu=p\int_0^\infty t^{p-1}\mu\{x:|f(x)|>t\}dt$$ 
and 
$$\int_{2^k}^{2^{k+1}}t^{p-1}\mu\{x:|f(x)|>t\}dt\le 2^{(k+1)p}\mu\{x:|f(x)|>2^k\}.$$
