Independence Theories and Generalized Zero-One Laws
In this paper an abstract characterization of the properties of independent events is given with examples from topology, probability, and Baire structures. Using this notion of independence, proofs of the Hewitt-Savage and Kolmogorov zero-one laws are given which include the probabilistic case and the topological cases considered by Oxtoby, Christensen, and K. P. S. and M. Bhaskara Rao.
Stout, Lawrence, "Independence Theories and Generalized Zero-One Laws" (1977). Scholarship. 84.