The chapter deals with the weak duality between two sub-Markovian resolvents on a Lusin topological space, with respect to a given measure m. This frame covers the probabilistic context of two Borel right processes in weak duality, which will be presented in Section 7.7. The main results of the first three sections are related to the coincidence of the m-semipolar and m-cosemipolar sets, the Revuz correspondence generated by the measures charging no cofinely open m-polar set. Section 7.4 develops, under the weak duality hypothesis, the subordination procedures from Chapter 5. In Section 7.5 we expose the preliminary results on the semi-Dirichlet forms, starting with a sub-Markovian resolvent of kernels satisfying the strong sector condition. Section 7.6 relates the transient semi-Dirichlet forms with the weak duality as it is presented in the first part of the chapter.