I have been studying the construction of the Martin boundary on a discrete set $X$ admitting an irreducible transient random walk $(X,P)$ from Wolfgang Woess' book titled "Random Walks on Infinte Graphs and Groups", where I came across the Poisson-Martin representation theorem which has been stated below:

For every positive harmonic function $h$ on a $X$, there is a positive Borel measure $\nu^h$ on the Martin boundary $\mathcal{M}$ of $X$ such that $$h(x)=\int_{\mathcal{M}} K(x,.) \mathrm{d} \nu^h$$ where $K(.,.)$ denotes the Martin kernel corresponding to $(X, P)$.

I also read about the Martin boundary on the Encyclopedia of Mathematics, where it is stated that for certain choices of $X$ (say $X$ is a bounded domain in $\mathbb{R}^n$ or a Green space), the Borel measure $\nu^h$ is actually a Radon measure. One question that intrigues me is whether we can always expect the Borel measure $\nu^h$ occurring in the above theorem to be a Radon measure? If not, can we expect that $\nu^h$ is a finite measure on $\mathcal{M}$? Is it finite on any compact subset of $\mathcal{M}$? Any help or reference is deeply appreciated. Thanks in advance!