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ChromeGames (talk | contribs) m Changing short description from "Whose value is zero for negative numbers and one for positive numbers" to "function whose value is zero for negative numbers and one for positive numbers" (Shortdesc helper) |
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These limits hold [[pointwise]] and in the sense of [[distribution (mathematics)|distributions]]. In general, however, pointwise convergence need not imply distributional convergence, and vice versa distributional convergence need not imply pointwise convergence. (However, if all members of a pointwise convergent sequence of functions are uniformly bounded by some "nice" function, then [[Lebesgue dominated convergence theorem|convergence holds in the sense of distributions too]].)
In general, any [[cumulative distribution function]] of a [[continuous distribution|continuous]] [[probability distribution]] that is peaked around zero and has a parameter that controls for [[variance]] can serve as an approximation, in the limit as the variance approaches zero. For example, all three of the above approximations are [[cumulative distribution function|cumulative distribution functions]] of common probability distributions:
==Integral representations==
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