theorem Th76: :: MESFUN15:74

for f being PartFunc of REAL,REAL
for a, b being Real
for A being non empty Subset of REAL st [.a,b.[ c= dom f & A = [.a,b.[ & f is_right_improper_integrable_on a,b & abs f is_right_ext_Riemann_integrable_on a,b & f | A is nonnegative holds
( f | A is_integrable_on L-Meas & right_improper_integral (f,a,b) = Integral (L-Meas,(f | A)) )