Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps.
J. Math. Soc. Japan
73(2):
525-551
(April, 2021).
DOI: 10.2969/jmsj/82398239
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