The positivity properties of an adelic Cartier divisor, such as arithmetic volumes, heights of algebraic points, etc., are of essential importance for applying theorems in Arakelov geometry to problems in number theory. In order to study the positivity of adelic Cartier divisors, I introduce a notion of pairs of adelic Cartier divisors and base conditions. In this talk, I will explain the motivation to introduce the notion of pairs and the differentiability property of the arithmetic volume function defined on the space of pairs along the directions defined by base conditions (http://arxiv.org/abs/1807.11680).