Class Field Theory
《Class Field Theory》 · 第 330 页 · Chapter 11，Section 11.6「The Weyl Integral Formula」，Theorem 11.30
Theorem 11.30 (Weyl Integral Formula). For all continuous functions $f$ on $K$, we have $\int_K f(x)\,dx = \frac{1}{|W|} \int_T \rho(t) \int_{K/T} f(yty^{-1})\,d[y]\,dt$, where $dx$, $dt$, and $d[y]$ are the normalized, left-invariant volume forms on $K$, $T$, and $K/T$, respectively and $|W|$ is the order of the Weyl group.