upper semicontinuous function

upper semicontinuous function

[′əp·ər ¦sem·i·kən′tin·yə·wəs ′fəŋk·shən]
(mathematics)
A real-valued function ƒ(x) is upper semicontinuous at a point x0 if, for any small positive ε, ƒ(x) always is less than ƒ(x0) + ε for all x in some neighborhood of x0.
References in periodicals archive ?
Let [phi]: [R.sub.+] [right arrow] [R.sub.+] be a nondecreasing and upper semicontinuous function. Then the following two conditions are equivalent:
([P.sup.2]) for fixed u, it is an upper semicontinuous function of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
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