Error Exponents for Hypothesis Testing of the General Source

In this correspondence, we consider the simple hypothesis testing problems for general sources in the sence of Han and Verdu. Re- cently 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 on the first-kind of error probability , where 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.