theorem :: MESFUN11:60

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f being PartFunc of X,ExtREAL
for c being Real st f is_simple_func_in S & f is nonpositive holds
( Integral (M,(c (#) f)) = (- c) * (integral' (M,(- f))) & Integral (M,(c (#) f)) = - (c * (integral' (M,(- f)))) )