As other people pointed out, it is probability using the L2 norm versus the standard probability that preserves the L1 norm. This means the following: Standard

As other people pointed out, it is probability using the L2 norm versus the standard probability that preserves the L1 norm. This means the following: Standard probability distributions are vectors that sum to 1. I.e. x=[0.5 0.2 0.3] is a probability distribution because each x(i)>=0 and sum x(i)=1. This means that the l1 norm of distribution vectors is always 1. The L2 norm of a vector is the square root of the sum of the entries squared. Hence a distribution would be a vector x(i) such that sum x(i)^2 is one. This allows x(i) to have both negative and even imaginary numbers. This awesome talk by Scott http://www.scottaaronson.com/blog/?p=1345 http://www.scottaaronson.com/blog/?p=1345 explains the difference between L1 and L2 probability using the Latke vs Hamentaschen Farsical debate. See the video from the link.