Classical Potential Theory and Its Probabilistic Counterpart

 From the contents: Introduction.- Notation and Conventions.- Part I Classical and Parabolic Potential Theory: Introduction to the Mathematical Background of Classical Potential Theory; Basic Properties of Harmonic, Subharmonic, and Superharmonic Functions; Infirma of Families of Suerharmonic Functions; Potentials on Special Open sets; Polar sets and Their Applications; The Fundamental Convergence Theorem and the Reduction Operation; Green Functions; The Dirichlet Problem for Relative Harmonic Functions; Lattices and Related Classes of Functions; The Sweeping Operation, The Fine Topology; The Martin Boundary; Classical Energy and Capacity; One-Dimensional Potential Theory.- .... Part II Probabilistic Counterpart of Part I.......- Part III Lattices in Classical Potential Theory and Martingale Theory; Brownian Motion and the PWB Method; Brownian Motion on the Martin Space.- Appendixes.