A plausibility-augmented imprecise-probability model updates via sampling (plausibilistic Bayes) or inequalities and proves almost-sure convergence of beliefs to the true probability.
K., An Introduction to Real Analysis , https://www.math.ucdavis.edu/ hunter/m125a/intro analy- sis.pdf
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Learning Probabilities: Towards a Logic of Statistical Learning
A plausibility-augmented imprecise-probability model updates via sampling (plausibilistic Bayes) or inequalities and proves almost-sure convergence of beliefs to the true probability.