  Iwasawa first established a duality relating the direct limit and the inverse
limit of class groups in a $\mathbb{Z}_p$-extension, and this result has
recently been extended to multiple $\mathbb{Z}_p$-extensions by many authors.
In this paper, we establish an analogous duality for the direct limit and the
inverse limit of higher even $K$-groups in a $\mathbb{Z}_p^d$-extension.
