▁Division ▁players ▁Category : E er ste ▁Div isie ▁players ▁Category : Associ ation ▁football ▁mid field ers ▁Category : Bel g ian ▁exp atri ate ▁football ers ▁Category : Bel g ian ▁exp atri ate ▁sports people ▁in ▁the ▁Netherlands ▁Category : Ex pat ri ate ▁football ers ▁in ▁the ▁Netherlands <0x0A> </s> ▁In ▁mathematics , ▁Wiener ' s ▁lemma ▁is ▁a ▁well - known ▁identity ▁which ▁rel ates ▁the ▁asympt otic ▁behaviour ▁of ▁the ▁Fourier ▁coefficients ▁of ▁a ▁Bor el ▁measure ▁on ▁the ▁circle ▁to ▁its ▁atomic ▁part . ▁This ▁result ▁adm its ▁an ▁analog ous ▁statement ▁for ▁measures ▁on ▁the ▁real ▁line . ▁It ▁was ▁first ▁discovered ▁by ▁Nor bert ▁Wiener . ▁ ▁Stat ement ▁ ▁Given ▁a ▁real ▁or ▁complex ▁Bor el ▁measure ▁ ▁on ▁the ▁unit ▁circle ▁, ▁let ▁ ▁be ▁its ▁atomic ▁part ▁( mean ing ▁that ▁ ▁and ▁ ▁for ▁. ▁Then ▁ ▁where ▁ ▁is ▁the ▁- th ▁Fourier ▁coefficient ▁of ▁. ▁▁ ▁Similarly , ▁given ▁a ▁real ▁or ▁complex ▁Bor el ▁measure ▁ ▁on ▁the ▁real ▁line ▁ ▁and ▁called ▁ ▁its ▁atomic ▁part , ▁we ▁have ▁ ▁where ▁ ▁is ▁the ▁Fourier ▁transform ▁of ▁. ▁ ▁Proof ▁ ▁First ▁of ▁all , ▁we ▁observe ▁that ▁if ▁ ▁is ▁a ▁complex ▁measure ▁on ▁the ▁circle ▁then ▁ ▁with ▁. ▁The ▁function ▁ ▁is ▁bounded ▁by ▁ ▁in ▁absolute ▁value ▁and ▁has ▁, ▁while ▁ ▁for ▁, ▁which ▁converges ▁to ▁ ▁as ▁. ▁Hence , ▁by ▁the ▁domin ated ▁convergence ▁theorem , ▁ ▁We ▁now