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Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

The term

**limit**comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

A

**theorem**is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a**theorem**is an embodiment of some general ...Given a sequence of real numbers a_n, the supremum

**limit**(also called the**limit**superior or upper**limit**), written lim sup and pronounced 'lim-soup,' is the**limit**of ...The

**limit**test, also sometimes known as the nth term test, says that if lima_n!=0 or this**limit**does not exist as n tends to infinity, then the series suma_n does not ...Given a sequence of real numbers a_n, the infimum

**limit**(also called the**limit**inferior or lower**limit**), written lim inf and pronounced 'lim-inf,' is the**limit**of ...A point v is a

**central**point of a graph if the eccentricity of the point equals the graph radius. The set of all**central**points is called the graph center.Let the least term h of a sequence be a term which is smaller than all but a finite number of the terms which are equal to h. Then h is called the lower

**limit**of the ...Let the greatest term H of a sequence be a term which is greater than all but a finite number of the terms which are equal to H. Then H is called the upper

**limit**of the ......