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Acknowledgement of priority

In the above paper several references to the existing literature were overlooked, some of which were in Japanese journals. In particular, the following points should be noted. 1. Theorem 5.1 appears in Nagasawa (1961) and the results of Section 4 (for compact 15) are included in Nagasawa (1961) and Nagasawa and Sato (1962). 2. Theorems 6.1 and 6.2 follow from Nelson (1958) who introduced general adjoints of Markov processes. These adjoint processes have the following meaning in the setting of Section 2 of the above paper. Consider the diffusion whose probability transition density p(t, x, y) is the minimal fundamental solution of a system (Gx , Bx ) , and let v(x)EC~(15) so that p*(t,x,y)= p(t, y, x)v(y)/v(x) is the minimal fundamental solution of the adjoint system (G~v, B~V). Then p*(t, x, y) is itself the probability transition density of a diffusion (called the adjoint process with respect to v) if and only if G *v ~ 0 and B*v ~O (that is, if and only if the constant term of G*v is non-positive and the constant term of B*v is non-negative). In this case the measure v(x) dax is called sub-invariant or excessive. Nelson shows that excessive measures always exist and that if the process is recurrent, then an excessive measure is unique and is in fact invariant. 3. In view of this earlier work, the above paper should be primarily regarded as an expository article on time-reversible diffusions based on the simple approach with an emphasis on applicability. Some references to other aspects of reversibility are given below.