## Möbius - Invariant Potential Theory in the Unit Ball of Cn |

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_is fr-sh Au(w BALL OF Cn compact set compact support continuous function Define a measure DOCTOR OF PHILOSOPHY equicontinuity exists f e f and g f e C(S finite measure fo-sh follows from Proposition Fubini's theorem g is radial g(cpz(w Haar measure harmonic majorant implies In-harmonic inequality Integrating in polar INVARIANT POTENTIAL THEORY is_an_ least to-harmonic majorant Lemma Lie groups lim f lim sup linear fractional transformations LP(S MOBIUS monotone convergence theorem neighborhood one-variable theory open set Pick polar coordinates proof of Proposition proof of Theorem Proposition 2.2 radial limits radial then f Riesz decomposition theorem subharmonic functions Suppose f Theorem 2.0 thesis tn-sh to-invariance to-sh functions trivial U-invariant uniformly unitary invariance University of Wisconsin upper semicontinuous weak compactness X(cpz(Ua Xe C(S z e Cn z e rB