Let $G$ be the group of rational points of a connected reductive group $\mathbb G$ defined over a non-archimedean local field $F$. For simplicity sake, I assume that $\mathbb G$ is split over $F$. Let $T$ the group of $F$-points of a maximal split torus of $\mathbb G$. Let $K$ be a good maximal compact subgroup of $G$ fixing a special vertex of the apartment of $T$. Let $\mu$ be the Haar measure on $G$ giving volume $1$ to $K$. My question is:

**Is there a closed formula for the measure $\mu (KtK)$, $t\in T$ ?**

In the case of ${\mathbb G}={\rm GL}(N)$, there is such a formula in Macdonald's book "Symmetric functions and Hall polynomials". But I need a reference in the general case.