# Sets and Probability

## TL;DR

This paper investigates the concept of random variables within set theory, focusing on what it means for a random set to have a certain probability of belonging to a predefined class of sets.

## Contribution

It introduces a novel perspective on random variables in set theory and explores their probabilistic properties within this framework.

## Key findings

- Defined the notion of random variables over set-theoretic universe
- Analyzed probabilities of random sets belonging to specific classes
- Provided foundational insights for probabilistic set theory

## Abstract

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.