# On the Laws of Large Numbers in Possibility Theory

## TL;DR

This paper extends the classical laws of large numbers into possibility theory, introducing possibilistic variants based on possibility measures and maxitive expectations, and demonstrates implications between weak and strong forms.

## Contribution

It provides novel possibilistic versions of the laws of large numbers, differing from previous work, and establishes that the weak law implies the strong law within this framework.

## Key findings

- Possibilistic variants of the laws of large numbers are formulated.
- Weak law implies the strong law in possibility theory.
- Results are based on possibility measure and maxitive expectation concepts.

## Abstract

In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are based on the possibility measure and on the "maxitive" definitions for possibility expectation and possibility variance. Also, we show that in this frame, the weak form of the law of large numbers, implies the strong law of large numbers.