theorem Th30: :: INTEGR25:30
for f being PartFunc of REAL,REAL
for b, c being Real st b >= c & right_closed_halfline c c= dom f & f is_+infty_improper_integrable_on c holds
( f is_+infty_improper_integrable_on b & ( improper_integral_+infty (f,c) = infty_ext_right_integral (f,c) implies improper_integral_+infty (f,b) = infty_ext_right_integral (f,b) ) & ( improper_integral_+infty (f,c) = +infty implies improper_integral_+infty (f,b) = +infty ) & ( improper_integral_+infty (f,c) = -infty implies improper_integral_+infty (f,b) = -infty ) )