introduce *the harmonic measure of the set $D$*, which describes the distribution of $X_{{\tau_D}}$ started from $x$ on $\{ {\tau_D}< \infty \}$. Namely, for any borel $A \subset {\mathbb{R}}$, $$P_D(x,A) = {\mathbb{P}}^x \big( X_{{\tau_D}} \in A \big).$$ If the density kernel of $P_D$ exists then we call it *the Poisson kernel* for the set $D$ and denote by the same symbol $P_D(x,z)$. The celebrated Ikeda-Watanabe formula [@IW62] provides a connection between the Poisson kernel and the Green function: $$P_D(x,A) = \int_D \nu(A-y)\,G_D(x,dy), \quad A \subset \overline{D}^c.$$ Finally, we say that a Borel measurable function $u$ is *harmonic* in an open set $D$ with respect to $\mathbf{X}$, if for any bounded open set $B$ such that $\overline{B} \subset D$, $$u(x) = {\mathbb{E}}^x u \big( X_{\tau_B} \big), \quad x \in B.$$ If the equality above holds also for $B=D$ then we say that $u$ is *regular harmonic* in $D$ (with respect to $\mathbf{X}$). Also, $u$ is *(regular) coharmonic in $D$* if it is (regular) harmonic in $D$ with respect to the dual process $\widehat{\mathbf{X}}$. Clearly, for symmetric processes a harmonic function is coharmonic and vice versa; in general, that is not necessarily true. We remark that by the strong Markov property, a 