MTH631Topic 98 Complex analysis Lectures Bounded Functions

MTH631Topic 98 Complex analysis Lectures Bounded Functions
The denitions of bounded above, bounded below, and bounded on a set S are the
same for functions of n variables as for functions of one variable, as are the denitions
of supremum and inmum of a function on a set S
Theorem: If f is continuous on a compact set S in Rn, then f is bounded on S.
Theorem: Let f be continuous on a compact set S in Rn and
α = inf
X∈S
f(X), β = sup
X∈S
f(X)

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