On the mean value property of finely harmonic and finely hyperharmonic functions |
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Authors: | B Fuglede |
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Institution: | (1) Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark |
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Abstract: | Summary It is shown that a finely superharmonic function in a planar fine domainU is greater than or equal to its lower integral with respect to harmonic measure associated with any bounded finely open setV with fine closure contained inU. Examples are given showing that this result does not extend to dimension 3 or more (unlessf is supposed to be, e.g., lower bounded onV) and also that the integral need not exist. |
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Keywords: | Primary 31A99 31B99 |
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