:: deftheorem defines is_integrable_on MESFUNC5:def 17 :
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 holds
( f is_integrable_on M iff ( ex A being Element of S st
( A = dom f & f is A -measurable ) & integral+ (M,(max+ f)) < +infty & integral+ (M,(max- f)) < +infty ) );