theorem Th58: :: MESFUN15:56

for f being PartFunc of REAL,REAL
for a, b being Real st a < b & ].a,b.] c= dom f & f is_left_improper_integrable_on a,b & abs f is_left_ext_Riemann_integrable_on a,b holds
( f is_left_ext_Riemann_integrable_on a,b & left_improper_integral (f,a,b) <= left_improper_integral ((abs f),a,b) & left_improper_integral ((abs f),a,b) < +infty )