# On systems of non-overlapping Haar polynomials

## TL;DR

This paper proves that the logarithm of n acts as an almost everywhere convergence Weyl multiplier for orthonormal systems of non-overlapping Haar polynomials and general martingale difference polynomials.

## Contribution

It establishes the convergence properties of Haar polynomial systems and extends results to general martingale difference polynomials.

## Key findings

- Log n is an almost everywhere convergence Weyl multiplier.
- Convergence results hold for general systems of martingale difference polynomials.

## Abstract

We prove that $\log n$ is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials.