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Definition: We denote by L(I) the set of all functions f of the form f=u-v, where u is in U(I) and v is in U(I). Each function f in L(I) is said to be Lebesgue-integrable on I, and its integral is defined by the equation int(f)=int(u) - int(v) where each integral is taken over I.
Source: Mathematical Analysis, second edition by Tom M. Apostol