A. D. Alexandrov's problem for non-positively curved spaces in the sense of Busemann

This paper is the last of a series devoted to the solution of Alexandrov's problem for non-positively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that isometries of a geodesically complete connected at infinity proper Busemann space $X$ are characterizied as follows: if a bijection $f\colon X\to X$ and its inverse $f^{-1}$ preserve distance 1, then $f$ is an isometry.