  We present a denotational semantics for higher-order probabilistic programs
in terms of linear operators between Banach spaces. Our semantics is rooted in
the classical theory of Banach spaces and their tensor products, but bears
similarities with the well-known Scott semantics of higher-order programs
through the use ordered Banach spaces which allow definitions in terms of fixed
points. Being based on a monoidal rather than cartesian closed structure, our
semantics effectively treats randomness as a resource.
