The previous notation which confused K and its boundary, defining K to be the contour and then talking about the interior of K or K-as-a-region to mean the region defined as the bounded region delimited by K-as-a-contour. The strength of the theorem is that the condition norm of f smaller than norm of g need only be verified on K-the-boundary and not K-the-region. This distinction is probably more important to emphasise than spare the few words, but on the other hand I am not satisfied of my edit. Maybe a good compromise would be to revert to the earlier phrasing but substitute K for delta K. 2017-02-02 UTC 18:28
Edit: This regards a change to the page on Rouché's Theorem 2018-02-12 UTC 18:59
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