AbstractIn case (Xn) is an i.i.d. sequence, and Sn = Xl + ··· + Xn, the Hsu-Robbins-Erdős theorem states that Σxn=1P(|Sn| >nϵ) < ∞, ϵ > 0, iff EX21 < ∞ and EX1 = 0. The purpose of this paper is to generalize this result to the case in which the steps Xn are independent, but their distributions are taken from a finite set
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
AbstractLet X1, X2,… be a sequence of i.i.d. random variables and Sn their partial sums. Necessary a...
Abstract Let U (n) denote the maximal length arithmetic progression in a non-uniform ran-dom subset ...
AbstractIn case (Xn) is an i.i.d. sequence, and Sn = Xl + ··· + Xn, the Hsu-Robbins-Erdős theorem st...
AbstractThe Hsu-Robbins-Erdős law of large numbers (1947, 1949) states that ifX1,X2,… are in...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. real-valued random variables and set Sn=∑i=1nXi, n⩾1....
AbstractLet {Xn}n≥1 be a sequence of independent and identically distributed random variables. For e...
AbstractFor a given sequence ω = (x(k))k=0∞ in Us, U = R/Z, let S(ω) denote the set of all boxes I i...
Let {Xn}n>=1 be a sequence of independent and identically distributed random variables. For each int...
AbstractLet Sn=X1+⋯+Xn be a random walk, where the steps Xn are independent random variables having ...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Delete the edges of a Kneser graph independently of each other with some probability: for what proba...
AbstractLet X1, X2, … be independent identically distributed random variables. Then, Hsu and Robbins...
One of the great appeals of Extremal Set Theory as a subject is that the statements are easily acces...
Abstract. Let {Xn, n 1} be a sequence of independent random variables with finite second moments an...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
AbstractLet X1, X2,… be a sequence of i.i.d. random variables and Sn their partial sums. Necessary a...
Abstract Let U (n) denote the maximal length arithmetic progression in a non-uniform ran-dom subset ...
AbstractIn case (Xn) is an i.i.d. sequence, and Sn = Xl + ··· + Xn, the Hsu-Robbins-Erdős theorem st...
AbstractThe Hsu-Robbins-Erdős law of large numbers (1947, 1949) states that ifX1,X2,… are in...
AbstractLet {X,Xn;n⩾1} be a sequence of i.i.d. real-valued random variables and set Sn=∑i=1nXi, n⩾1....
AbstractLet {Xn}n≥1 be a sequence of independent and identically distributed random variables. For e...
AbstractFor a given sequence ω = (x(k))k=0∞ in Us, U = R/Z, let S(ω) denote the set of all boxes I i...
Let {Xn}n>=1 be a sequence of independent and identically distributed random variables. For each int...
AbstractLet Sn=X1+⋯+Xn be a random walk, where the steps Xn are independent random variables having ...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Delete the edges of a Kneser graph independently of each other with some probability: for what proba...
AbstractLet X1, X2, … be independent identically distributed random variables. Then, Hsu and Robbins...
One of the great appeals of Extremal Set Theory as a subject is that the statements are easily acces...
Abstract. Let {Xn, n 1} be a sequence of independent random variables with finite second moments an...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
AbstractLet X1, X2,… be a sequence of i.i.d. random variables and Sn their partial sums. Necessary a...
Abstract Let U (n) denote the maximal length arithmetic progression in a non-uniform ran-dom subset ...
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