The relative entropy was introduced by Solomon Kullback and Richard Leibler in Kullback & Leibler (1951) as "the mean information for discrimination between H 1 and H 2 per observation from μ μ 1 ", where one is comparing two probability measures μ μ 1 , μ μ 2 , and H 1 , H 2 are the hypotheses that one is selecting from measure μ μ 1 , μ μ 2 (respectively). They denoted this by I ( 1 : 2 ) , and defined the "'divergence' between μ μ 1 and μ μ 2 " as the symmetrized quantity J ( 1 , 2 ) = I ( 1 : 2 ) + I ( 2 : 1 ) , which had already been defined and used by Harold Jeffreys in 1948. In Kullback (1959), the symmetrized form is again referred to as the "divergence", and the relative entropies in each direction are referred to as a "directed divergences" between two distributions; Kullback preferred the term discrimination information. The term "divergence" is in contrast to a distance (metric), since the symmetrized divergence does not satisfy the triangle inequality. Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in Kullback (1959, pp. 6–7, §1.3 Divergence). The asymmetric "directed divergence" has come to be known as the Kullback–Leibler divergence, while the symmetrized "divergence" is now referred to as the Jeffreys divergence.