Relative entropy is only defined in this way if, for all x, Q ( x ) = 0 implies P ( x ) = 0 (absolute continuity). Otherwise, it is often defined as + ∞ ∞ , but the value + ∞ ∞ is possible even if Q ( x ) ≠ ≠ 0 everywhere, provided that X is infinite in extent. Analogous comments apply to the continuous and general measure cases defined below.