using direct limit argument in homology

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 $H_*(K(G,r);\mathbb Q)$?

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$H_*(K(V,r),\mathbb Q)=\lim_W H_*(K(W,r),\mathbb Q)$, where the limit is the direct limit taken with respect to the direct limit of all finite dimensional subspaces $W$ of $V$. –  Mariano Suárez-Alvarez Jun 8 '11 at 12:54
@ Mariano Suárez-Alvarez : thanks alot!! –  palio Jun 8 '11 at 13:10