In particular, if P ( d x ) = p ( x ) μ μ ( d x ) and Q ( d x ) = q ( x ) μ μ ( d x ) , then p ( x ) = q ( x ) μ μ - almost everywhere. The entropy H ( P ) thus sets a minimum value for the cross-entropy H ( P , Q ) , the expected number of bits required when using a code based on Q rather than P ; and the Kullback–Leibler divergence therefore represents the expected number of extra bits that must be transmitted to identify a value x drawn from X, if a code is used corresponding to the probability distribution Q, rather than the "true" distribution P.