# The sumset phenomenon

```@inproceedings{Jin2001TheSP,
title={The sumset phenomenon},
author={Renling Jin},
year={2001}
}```
Answering a problem posed by Keisler and Leth, we prove a theorem in non-standard analysis to reveal a phenomenon about sumsets, which says that if two sets A and B are large in terms of measure, then the sum A+B is not small in terms of order-topology. The theorem has several corollaries about sumset phenomenon in the standard world; these are described in sections 2-4. One of these is a new result in additive number theory; it says that if two sets A and B of non-negative integers have…
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