1 Excessive Functions.- 1.1 Sub-Markovian resolvent of kernels.- 1.2 Basics on excessive functions.- 1.3 Fine topology.- 1.4 Excessive measures.- 1.5 Ray topology and compactification.- 1.6 The reduction operation and the associated capacities.- 1.7 Polar and semipolar sets. Nearly measurable functions.- 1.8 Probabilistic interpretations: Sub-Markovian resolvents and right processes.- 2 Cones of Potentials and H-Cones.- 2.1 Basics on cones of potentials and H-cones.- 2.2 ?-Balayages on cones of potentials.- 2.3 Balayages on H-cones.- 2.4 Quasi bounded, subtractive and regular elements of a cone of potentials.- 3 Fine Potential Theoretical Techniques.- 3.1 Cones of potentials associated with a sub-Markovian resolvent.- 3.2 Regular excessive functions, fine carrier and semipolarity.- 3.3 Representation of balayages on excessive measures.- 3.4 Quasi bounded, regular and subtractive excessive measures.- 3.5 Tightness for sub-Markovian resolvents.- 3.6 Localization in excessive functions and excessive measures.- 3.7 Probabilistic interpretations: Continuous additive functionals and standardness.- 4 Strongly Supermedian Functions and Kernels.- 4.1 Supermedian functionals.- 4.2 Supermedian ?-quasi kernels.- 4.3 Strongly supermedian functions.- 4.4 Fine densities.- 4.5 Probabilistic interpretations: Homogeneous random measures.- 5 Subordinate Resolvents.- 5.1 Weak subordination operators.- 5.2 Inverse subordination.- 5.3 Probabilistic interpretations: Multiplicative functionals.- 6 Revuz Correspondence.- 6.1 Revuz measures.- 6.2 Hypothesis (B) of Hunt.- 6.3 Smooth measures and sub-Markovian resolvents.- 6.4 Measure perturbation of sub-Markovian resolvents.- 6.5 Probabilistic interpretations: Positive left additive functionals.- 7 Resolvents under Weak Duality Hypothesis.- 7.1Weak duality hypothesis.- 7.2 Natural potential kernels and the Revuz correspondence.- 7.3 Smooth and cosmooth measures.- 7.4 Subordinate resolvents in weak duality.- 7.5 Semi-Dirichlet forms.- 7.6 Weak duality induced by a semi-Dirichlet form.- 7.7 Probabilistic interpretations: Multiplicative functionals in weak duality.- A Appendix.- A.1 Complements on measure theory, kernels, Choquet boundary and capacity.- A.2 Complements on right processes.- A.4 Basics on coercive closed bilinear forms.- Notes.
