Structure Theory of Set Addition III. Results and Problems

TL;DR

This paper explores the structure of sets in integer lattices with small doubling properties, focusing on theorems about set volume and related problems in additive combinatorics.

Contribution

It advances the understanding of set structure in additive combinatorics by analyzing volume theorems and addressing open problems in the field.

Findings

Theorem on volume bounds for sets with small doubling

Identification of key problems in the structure theory of set addition

Discussion of open problems and future directions in additive combinatorics

Abstract

We are discussing the theorem about the volume of a set $A$ of $Z^n$ having a small doubling property $|2A| < Ck, k=|A|$ and oher problems of Structure Theory of Set Addition (Additive Combinatorics).