Geodesic
The mean value theorem for harmonic functions in a domain of Hilbert space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 32-35

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We prove that the value of any harmonic function whose domain is an open set in the Hilbert space in a given point $x$ is equal to the mean value of the function with respect to a measure given on a ball with the centre $x$. From this we derive a theorem of Liouville that says that a bounded harmonic function defined in all points of a Hilbert space is constant. 
@article{VMUMM_1982_5_a8,
     author = {A. A. Belyaev},
     title = {The mean value theorem for harmonic functions in a domain of {Hilbert} space},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {32--35},
     publisher = {mathdoc},
     number = {5},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/}
}
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A. A. Belyaev. The mean value theorem for harmonic functions in a domain of Hilbert space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 32-35. http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/