Alessandra Marzola: A categorical interpretation of random variables. Diplom thesis, Ferrara 1987. Original title: Un approccio intrinseco alla probabilità.

INTEGRATION IN A SIGMA-ALGEBRA Boolean algebras and sigma-algebras Riesz spaces Daniell integrals Beppo Levi's theorem Completion of an integral and identifiable integrals The Daniell integral generated by an additive set function Tensor product of sigma-algebras The Riesz space Random(A,R) The theorem of Radon-Nikodym Transformations of integrals and induced integrals FUNDAMENTAL CONCEPTS OF PROBABILITY THEORY Events and random variables in the sense of Kolmogorov Probability spaces and distribution of a random variable Mean value of a random variable Concepts of convergence Independence Limit theorems Conditional mean and conditional probability CATEGORICAL CONSTRUCTIONS The language of categories Left finitely complete categories A CONCEPT OF RANDOM VARIABLE Environment and chance Topoi The algebra of imaginations The election of the president of the United States and calculating gain REFERENCES