### On the integral representation of finely superharmonic functions

In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset $U$ of a Brelot $\mathcal{P}$-harmonic space $\Omega $ with countable base of open subsets and satisfying the axiom $D$. When $\Omega $ satisfies the hypothesis of uniqueness, we define the Martin boundary of $U$ and the Martin kernel $K$ and we obtain the integral representation of invariant functions by using the kernel $K$. As an application of the integral representation we extend to the cone $\mathcal{S}\left(\mathcal{U}\right)$ of nonnegative...