:: deftheorem Def8 defines infty_ext_left_integral INTEGR10:def 8 :
for f being PartFunc of REAL,REAL
for b being Real st f is_-infty_ext_Riemann_integrable_on b holds
for b₃ being Real holds
( b₃ = infty_ext_left_integral (f,b) iff ex Intf being PartFunc of REAL,REAL st
( dom Intf = left_closed_halfline b & ( for x being Real st x in dom Intf holds
Intf . x = integral (f,x,b) ) & Intf is convergent_in-infty & b₃ = lim_in-infty Intf ) );