Let $K$ be a compact set in the complex plane and let $f$ be a function holomorphic on the complement $\Omega$ of $K$ and vanishing at infinity. We prove that there are finite complex-valued Borel measures $\mu_{m, n} (m, n = 0, 1, 2,\ldots; m + n \geqslant 1)$ on $K^2$ satisfying $\lim_{k \rightarrow \infty}(\sum_{m + n = k}\|\mu_{m, n}\|)^{1/k} = 0$ so that $$f(z) = \sum_{m, n} \int_{K^2}(z - w_1)^{-m}(z - w_2)^{-n}d\mu_{m, n}(w_1, w_2) \quad(z \in \Omega).$$