Indexed on: 01 Dec '78Published on: 01 Dec '78Published in: Probability Theory and Related Fields
In this paper the following generalization of a theorem by B.R. Gelbaum is proved:Let (K, d) be a compact, connected metric space. Let B denote the Borel sets of (K, d), and P be a probability measure on B with P(G)≠O for any nonempty open G, f, gεC(K,d) independent random variables on (K,B,P) and let g satisfy the following assumption:There is an yo∃ℝ such that g−1(y0) is a finite nonempty set. Then f is a constant function.Examples show that the assumptions of this theorem are essential.