I saw the result below without a proof and I would like to see it.
Result: Let $g$ a nonnegative and measurable function in $\Omega$ and $\mu_{g} $ its distribuction function, i.e., \begin{equation} \mu_{g}(t)= |\{x\in \Omega : g(x)>t\}|, t>0. \end{equation} Let $\eta>0$ and $M>1$ be constants. Then, for $0
\begin{equation} g \in L^{p}(\Omega) \Leftrightarrow \sum_{k\ge 1} M^{pk} \mu_{g}(\eta M^k) = S < \infty. \end{equation}