Ethan Zuckerman proposes measuring attention with a unit of measure called a Kardashian. One Kardashian is equal to the amount of worldwide media attention that Kim Kardashian gets in a day.
I choose the Kardashian as a unit both because I like the mitteleuropean feel of the term -- like the Ohm or the Roentgen -- and because Kardashian is an exemplar of attention disconnected from merit, talent or reason. The Kardashian mentions how much attention is paid, not how much attention is deserved, so naming the unit after someone who is famous for being famous seems appropriate. Should the unit be adopted, I would hope that future scholars will calculate Kardashians using whatever public figure is appropriate at the time for being inappropriately famous.
Example usage: The crisis in Greece received 12 microKardashians of attention today.