Limit Distributions for Sums of Independent Random Variables

according application attraction belongs called chapter characteristic function chosen complete conclude consequently consider constants converge corresponding defined definition denote density determined dFnk dFnx dG(y distribution function domain elementary equal equation example exists expectations fact finite follows formula given gives Hence holds independent independent random variables inequality infinitely divisible law infinitesimal integral interval Khintchine LEMMA limit limit distribution limit law limit theorems mathematical means measure natural necessary and sufficient normal law obtained Poisson possible preceding probability problem Proof properties proved random variables relation remark requirement respect satisfied sequence space stable law sufficiently large summands sums suppose theorem theory tion Translator's note values variance