Error exponents for hypothesis testing of the general source

In this correspondence, we consider the simple hypothesis testing problems for general sources in the sense of Han and Verdu. Recently Han established a compact formula for the supremum of achievable exponents for the second-kind of error probability under the asymptotic constraint of the form mu_n ~ e^-nr (n rarr infin) on the first-kind of error probability mu_n, where r is a given positive number. We investigate the same hypothesis testing problems studied by Han. The aim of the correspondence is to give a new expression for the supremum of achievable error exponents. Our formula is expressed in terms of the divergences and given in quite different forms from Han´s expression