Abstract
A real-valued function f f defined on an open subset of R N {R^N} is said to have the restricted mean value property with respect to balls (spheres) if, for each point x x in the set, there exists a ball (sphere) with center x x and radius r ( x ) r(x) such that the average value of f f over the ball (sphere) is equal to f ( x ) f(x) . If f f is harmonic then it has the restricted mean value property. Here new conditions for the converse implication are given.
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