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Solve ASAP

Let v be a reasure on a c -field F on 1 and f and g be Borel functions with respeto F. Show that (i) if | fdv exists and a R, then S (af)dv exists and is equal to a fdv; (ii) if both S fdv and S gdy exist and S fdv + S gdy is well defined, then S(f +g)dv exists and is equal to fdv + S gdv. Note. For integrals in calculus, properties such as S(af)dv=a fdv and S (f + g)dv fdv + S gdy are obvious. However, the proof of them are complicated for integrals defined on general measure spaces. As shown in this exercise, the proof often has to be broken into several steps: simple functions, nonnegative functions, and then general functions. ( 1