:: deftheorem defines summable_set BHSP_6:def 2 :
for X being RealUnitarySpace
for Y being Subset of X holds
( Y is summable_set iff ex x being Point of X st
for e being Real st e > 0 holds
ex Y0 being finite Subset of X st
( not Y0 is empty & Y0 c= Y & ( for Y1 being finite Subset of X st Y0 c= Y1 & Y1 c= Y holds
||.(x - (setsum Y1)).|| < e ) ) );