Let $D\subset\mathbb R^n$ be connected and open. A function $f:D\to \mathbb R$ is harmonic if for all $z\in D$ and every $\varepsilon > 0$ with $\text{dist}(z,\partial D) > \varepsilon$, then $f(z) = MV(f,z,\varepsilon)$ where $\partial D$ denotes the boundary of $D$ and $MV$ denotes the circular mean value.
Equivalently, a function $f$ is harmonic if its Laplacian is 0.
Wikidata ID: Q599027