lower semicontinuous function

lower semicontinuous function

[¦lō·ər ‚sem·ē·kən′tin·yə·wəs ‚fənk·shən] (mathematics) A real-valued function ƒ(x) is lower semicontinuous at a point x0 if, for any small positive number ε, ƒ(x) is always greater that ƒ(x0) - ε for all x in some neighborhood of x0.