## Potential theory: selected topics, Issue 1633The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis. |

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### Contents

Preface | 3 |

The Physical background of Potential theory | 10 |

Hausdorff measures and capacities | 29 |

Copyright | |

15 other sections not shown

### Common terms and phrases

Aikawa analytic capacity analytic sets approximately everywhere arbitrary assume balls Borel set boundary bounded Ca(F capacitable capacitary measure CK(E CK(F Ck{E compact set compact subset compact support Const convergence Corollary countable dD with respect define Definition denote dfi(y dimension energy integral equilibrium measure estimate exists a measure finite Gfi(x Green energy Green function Green potential harmonic function harmonic measure harmonic minorant Hausdorff measure Hence holds implies kernel Lecture Notes Let F Let Q liminf limsup Lipschitz domain Math maximum principle Mh(E minimally thin nonnegative superharmonic function Observe obtain oo oo open set Poisson integral positive constant positive harmonic function potential theory proof of Theorem properties quasiadditivity reduced function Remark required inequality respect to measure Riesz sequence signed measure subadditive Suppose thin at dD universally measurable set Wa(F Whitney cubes Whitney decomposition