Definition talk:Simple Function

What's the benefit of providing the same definition for both real-number and non-real-number domains? From what I can tell, the definition is identical, even down to the difference that one invokes the term "lebesgue measurable"? (As even "lebesgue measurable" is exactly the same thing as "measurable" except that its domain is the set of real numbers.) --prime mover 02:21, 23 March 2012 (EDT)