It states that consider a rational function F(s). Consider a region in s plane such that no singularities i.e. poles lie within or on the boundary of the region. Then the function F(s) attains maximum magnitude in that region on the boundary and this maximum is bounded.If |F(s)| attains maximum value on a boundary, then theorem may be applied to |1/F(s)| and it can be shown that |F(s)| attains its minimum value in the region on the boundary, provided there are no zeros within or on the boundary of the region.
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