Let $g$ be nonnegative and measurable function in $\Omega$ and $\mu_{g}$ be its distribution function, i.e.,$$\mu_{g}(t)=\left|\left\{ x\in \Omega:g(x)>t\right\}\right|,\; t>0.$$Let $\eta>1$ and $M>1$ be constants. Then, for $0<p<\infty$,$$g\in L^{p}(\Omega)\iff \sum_{k\geq1}M^{pk}\mu_{g}(\eta M^{k})=S<\infty$$and$$C^{-1}\leq \left\|g\right\|_{L^{p}(\Omega)}^{p}\leq\left(\left|\Omega\right|+S\right),$$where $C>0$ is a constant depending only on $\eta, M$ and $p$.
Any help will be appreciated.