On a Theorem of Plünnecke Concerning the Sum of A Basis and A Set of Positive Density Original Research Article

In 1935 Erdimages proved that every additive basis image of order h is an essential component by showing σ(image + image) ≥ σ(image) + (1/2h) σ(image)(1 − σ(image)), where σ denotes Schnirelmann density. This lower bound was improved by Plünnecke to σ(image + image) ≥ σ(image)1 − 1/h, giving the best exponent. A simplified proof is presented.