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