# The EL Theorem

## TL;DR

The paper presents a theorem relating the universal probability of string sets to the maximum probability of individual strings, bounded by the information about the halting sequence.

## Contribution

It introduces the EL Theorem, connecting universal probability sums over sets with maximum individual probabilities and halting sequence information.

## Key findings

- Universal probability of sets approximates maximum string probability
- Difference bounded by halting sequence information
- Provides insights into algorithmic probability and complexity

## Abstract

The combined universal probability $\mathbf{m}(D)$ of strings $x$ in sets $D$ is close to max $\mathbf{m}(x)$ over $x$ in $D$: their logs differ by at most $D$'s information $\mathbf{I}(D:\mathcal{H})$ about the halting sequence $\mathcal{H}$.