Title: The Topology of Statistical Verifiability,
Abstract: Topological models of empirical and formal inquiry are increasingly
prevalent. They have emerged in such diverse fields as domain theory [1, 16],
formal learning theory [18], epistemology and philosophy of science [10, 15, 8,
9, 2], statistics [6, 7] and modal logic [17, 4]. In those applications, open
sets are typically interpreted as hypotheses deductively verifiable by true
propositional information that rules out relevant possibilities. However, in
statistical data analysis, one routinely receives random samples logically
compatible with every statistical hypothesis. We bridge the gap between
propositional and statistical data by solving for the unique topology on
probability measures in which the open sets are exactly the statistically
verifiable hypotheses. Furthermore, we extend that result to a topological
characterization of learnability in the limit from statistical data.