theorem Th57: :: MESFUN15:55

for f being PartFunc of REAL,REAL
for a, b being Real st a < b & [.a,b.[ c= dom f & f is_right_improper_integrable_on a,b & abs f is_right_ext_Riemann_integrable_on a,b holds
( f is_right_ext_Riemann_integrable_on a,b & right_improper_integral (f,a,b) <= right_improper_integral ((abs f),a,b) & right_improper_integral ((abs f),a,b) < +infty )