Is periodicity defined as the fact that elements increase in atomic mass in a regular way?
No, the periodicity of the Periodic Table of Elements refers to the fact that the chemical properties of elements vary in a periodic way, from metals on the left hand side of the table to non-metals and then to noble gases in the far right hand column. Each row goes through the same variations. There is nothing periodic about the increase in mass; that would be described as a linear progression rather than a periodic phenomenon.
