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Bernstein's theorem

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  1. a term from functional analysis

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
  2. a branch of mathematics, Bernstein's theorem states that any real-valued function on the half-line [0, ∞) that is totally monotone is a mixture of exponential functions

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
  3. In one important special case the mixture is a weighted average, or expected value

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
  4. Total monotonicity (sometimes also complete monotonicity) of a function f means that for all nonnegative integers n and for all t ≥ 0

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
  5. Another convention puts the opposite inequality in the above definition

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
  6. Completely monotone functions are also called Bernstein functions

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on February 16, 2009
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