| Compact Support |
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In particular, in Probability Theory , the support of a Probability Distribution is the closure of the set of possible values of a random variable having that distribution. COMPACT SUPPORT Functions with compact support in ''X'' are those with support that is a Compact subset of ''X''. For example, if ''X'' is the real line, they are examples of functions that Vanish At Infinity (and negative infinity). Indeed, they are special cases of such functions that must vanish at finite bounds. In Good Cases , functions with compact support are Dense in the space of functions that vanish at infinity, but this property requires some technical work to justify in a given example. As an intuition for more complex examples, and in the language of Limits , for any ε > 0, any function ''f'' on the real line ''X'' that vanishes at infinity can be approximated by choosing an appropriate compact subset ''C'' of ''X'' such that |
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