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Functions with the restricted mean value property. (Chinese. English summary) Zbl 0693.31002
Summary: Let $$\Omega$$ be a Lipschitz domain in $$R^ N$$ (N$$\geq 3)$$, f be a continuous function on $$\Omega$$ with the restricted mean value property. A sufficient condition is given for f to be harmonic on $$\Omega$$.

##### MSC:
 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions