2995-3162ISSN (Online)
Volume 6 , Issue 1 , PP: 01-21, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Takaaki Fujita 1 * , Ajoy Kanti Das 2
Doi: https://doi.org/10.54216/PMTCS.060101
Standard probability theory assigns each event a single real value in [0, 1], satisfying non-negativity, normalization, and countable additivity. Hyper-Probability extends this notion by assigning to each event a set of probability values in [0, 1], thereby capturing multiple independent assessments from diverse sources. Super-HyperProbability further generalizes the framework by mapping events to iterated power sets of [0, 1], modeling hierarchical uncertainty across multiple aggregation levels. In this paper, we formally define the Hyper-Probability Measure and Hyper-Probability Distribution, examine their fundamental properties, and demonstrate how these constructs unify and extend classical probability within the Hyper- and Super-HyperProbability paradigms.
Probability , HyperProbability , SuperHyperProbability , Probability Distribution , Probability Measure
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