# Singular integral and differentiability properties of functions. Stein pp. 4.

Let $$g:\mathbb{R}^n\to\mathbb{R}$$ and let $$\lambda(\alpha)=m \left\{x:|g(x)|>\alpha\right\}$$ If $$g\in L^p$$. Why $$\int_{\mathbb{R}^n}|g(y)|^pdy=-\int_{0}^{\infty} \alpha^p d\lambda(\alpha)$$?

• Are you certain of your equality ? For example the left hand side is $\geq 0$ while the right hand side is $\leq0$. – Delta-u Apr 27 at 11:40