Theory of Probabilistic Connectedness

Yu-Lin Chou

No yb2u3, OSF Preprints from Center for Open Science

Abstract: We introduce and study a notion of probabilistic connectedness, which we term $proconnectedness$, defined in terms of partitions of a probability space into two nonempty disjoint independent events. Both proconnectedness and disproconnectedness are shown to be invariants (in a suitable sense) under isomorphic random elements. We show that a substantial part of the fundamental theory of topological connectedness admits a natural counterpart in the present theory of proconnectedness. Some applications and connections regarding limit theorems, cardinality equality of measurability structures, atomic distributions, and singular distributions are discussed.

Date: 2020-12-21
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:yb2u3

DOI: 10.31219/osf.io/yb2u3

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