Frechet bounds of the 1-st kind for sets of half-rare events

TL;DR

This paper investigates the properties of Frechet bounds of the first kind for sets of half-rare events, establishing key lemmas and corollaries about their nonzero values and probability distributions.

Contribution

It introduces new lemmas and corollaries regarding the nonzero values of Frechet bounds for half-rare events and generalizes these results to arbitrary event-probability distributions.

Findings

Proved that lower Frechet bounds of the first kind have at most two nonzero values for half-rare events.

Extended the results to sets of events with arbitrary probability distributions.

Provided properties and implications of Frechet bounds in probabilistic event sets.

Abstract

Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on the analogous assertion for sets of events with arbitrary event-probability distributions.