  Measurable cones, with linear and measurable functions as morphisms, are a
model of intuitionistic linear logic and of call-by-name probabilistic PCF
which accommodates ``continuous data types'' such as the real line. So far
however, they lacked a major feature to make them a model of more general
probabilistic programming languages (notably call-by-value and
call-by-push-value languages): a theory of integration for functions whose
codomain is a cone, which is the key ingredient for interpreting the sampling
programming primitives. The goal of this paper is to develop such a theory: our
definition of integrals is an adaptation to cones of Pettis integrals in
topological vector spaces. We prove that such integrable cones, with
integral-preserving linear maps as morphisms, form a model of Linear Logic for
which we develop two exponential comonads: the first based on a notion of
stable functions introduced in earlier work and thesecond based on a new notion
of integrable analytic function on cones.
