This paper was published in American Mathematical Monthly 99 (1992), 51-55.
Bôcher's Theorem characterizes the behavior of positive harmonic functions in the neighborhood of an isolated singularity. The usual proofs of Bôcher's Theorem rely either on the theory of superharmonic functions or series expansions using spherical harmonics. This paper offers a different and simpler approach to Bôcher's Theorem.
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The proof in this paper also appears in the authors' book Harmonic Function Theory.