## A Compactification Theory with Potential-theoretic Applications |

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### Contents

FUNCTIONAL COMPACTIFICATIONS OF LOCALLY | 55 |

Extreme Points and the Choquet Boundary | 65 |

A Representation Theorem | 69 |

3 other sections not shown

### Common terms and phrases

abstract M)-space belongs to Hm(R boundary ideal bounded harmonic function c,PR chapter Choquet boundary closed linear sublattice closed subset compact boundaries compact carrier compact Hausdorff space compact set compact space compact subset compactification s,S Consequently constant functions continuous function corollary 1.8 defined Dirichlet problem disjoint endpoint compactification exists an F extreme point F belongs F-constant F-unit finitary functions follows Freudenthal HA(R harmonic lattice harmonic majorant harmonic upper bound HB(R homeomorphism isomorphic and linearly lattice isomorphic lemma let F linear space linear subspace linearly isometric locally compact Hausdorff locally connected Math maximal ideal minimal functions open neighborhood open Riemann surface open set pointwise order Proof proposition 1.7 prove R U F real number Riemann surface satisfying second countable semicompact Hausdorff space semicompact space semicompactly imbedded semicompactly separated separates the points subharmonic function theorem topological space topology uniform norm z e G