suppose we know $H_*(K(\mathbb Q,r);\mathbb Q)$ and want to determine $H_*(K(G,r);\mathbb Q)$ where $G$ is a $\mathbb Q$-vector space.
if $G$ if finite dimensional then we can use $K(H_1\times H_2,r)= K(H_1,r)\times K( H_2,r)$ followed by a Kunneth formula. But when $G$ is a general $\mathbb Q$-vector space how do write a direct limit argument to determine $H_*(K(G,r);\mathbb Q)$?