Reference request: Measure theory books using $\omega(\alpha) = |\{f>\alpha\}|$

Question

I am working from Wheeden and Zygmund's Measure and Integral, and they prove theorems such as $\int_E f = -\int_{-\infty}^{+\infty} \alpha d\omega(\alpha)$ where $\omega(a) = |\{x: f(x)>\alpha\}|$ (and $|.|$ is the Lebesgue measure). Are there any other texts that use integrating against this function to work with the Lebesgue integral that I can look at?