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In mathematics, Carleman's condition is a sufficient condition for the determinacy of the Hamburger moment problem.To say that P is sufficient for Q is to say that in and of itself, knowing P to be true is adequate grounds to conclude that Q is true. The logical relation is expressed as "If P then Q" or "P Rightarrow Q," and may also be expressed as "P implies Q." Several sufficient conditions may, taken together, constitute a single necessary condition, as illustrated in example 3.Example 1: An occurrence of thunder is a sufficient condition for the occurrence of lightning in the sense that hearing thunder, and unambiguously recognizing it as such, justifies concluding that there has been a lightning bolt.