Geodesic
The final version of the mean value theorem for harmonic functions
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 351-358

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We construct examples of nonharmonic functions satisfying the mean value equation for some set of spheres. These results permit us to obtain the two-circle theorem in its definitive form. 
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     author = {V. V. Volchkov},
     title = {The final version of the mean value theorem for harmonic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {351--358},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a3/}
}
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V. V. Volchkov. The final version of the mean value theorem for harmonic functions. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 351-358. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a3/