Foundations of modern potential theory

 Content: 1. Spaces of measures and signed measures. Operations on measures and signed measures (No. 1-5).-   2. Space of distributions. Operations on distributions (No. 6-10)..-   3. The Fourier transform of distributions (No. 11-13).- I. Potentials and their basic properties.-   1. M. Riesz kernels (No. 1-3).-   2. Superharmonic functions (No. 4-5).-   3. Definition of potentials and their simplest properties (No. 6-9)...-   4. Energy. Potentials with finite energy (No. 10-15).-   5. Representation of superharmonic functions by potentials (No. 16-18).-   6. Superharmonic functions of fractional order (No. 19-25).- II. Capacity and equilibrium measure.-   1. Equilibrium measure and capacity of a compact set (No. 1-5).-   2. Inner and outer capacities and equilibrium measures. Capacitability (No. 6-10).-   3. Metric properties of capacity (No. 11-14).-  4. Logarithmic capacity (No. 15-18).- III. Sets of capacity zero. Sequences and bounds for potentials.-   1. Polar sets (No. 1-2).-   2. Continuity properties of potentials (No. 3-4).-   3. Sequences of potentials of measures (No. 5-8).-   4. Metric criteria for sets of capacity zero and bounds for potentials (No. 9-11).- IV. Balayage, Green functions, and the Dirichlet problem.-   1. Classical balayage out of a region (No. 1-6).-   2. Balayage for arbitrary compact sets (No. 7-11).-   3. The generalized Dirichlet problem (No. 12-14).-   4. The operator approach to the Dirichlet problem and the balayage problem (No. 15-18).-   5. Balayage for M. Riesz kernels (No. 19-23)...-   6. Balayage onto Borel sets (No. 24-25).- V. Irregular points.-   1. Irregular points of Borel sets. Criteria for irregularity (No. 1-6)...-  2. The characteristics and types of irregular points (No. 7-8)...-  3. The fine topology (No. 9-11).-   4. Properties of set of irregular points (No. 12-15).-   5. Stability of the Dirichlet problem. Approximation of continuous functions by harmonic functions (No. 16-22).- VI. Generalizations.-   1. Distributions with finite energy and their potentials (No. 1-5)...-  2. Kernels of more general type (No. 6-11).-   3. Dirichlet spaces (No. 12-15).- Comments and bibliographic references.