:: deftheorem Def4 defines right_improper_integral INTEGR24:def 4 :
for f being PartFunc of REAL,REAL
for a, b being Real st f is_right_improper_integrable_on a,b holds
for b₄ being ExtReal holds
( b₄ = right_improper_integral (f,a,b) iff ex Intf being PartFunc of REAL,REAL st
( dom Intf = [.a,b.[ & ( for x being Real st x in dom Intf holds
Intf . x = integral (f,a,x) ) & ( ( Intf is_left_convergent_in b & b₄ = lim_left (Intf,b) ) or ( Intf is_left_divergent_to+infty_in b & b₄ = +infty ) or ( Intf is_left_divergent_to-infty_in b & b₄ = -infty ) ) ) );