#### Title

A functional limit theorem for Erdös and Rényi's law of large numbers

#### Document Type

Article

#### Publication Title

Probability Theory and Related Fields

#### Publication Date

3-1-1994

#### Abstract

We use the theory of large deviations on function spaces to extend Erdös and Rényi's law of large numbers. In particular, we show that with probability 1, the double-indexed set of paths {WN, n} defined by {Mathematical expression} where {Mathematical expression}, {Xi:i≧1} is an iid sequence of random variables, and h(N)=[clog N] is relatively compact; the limit set is given by the set [x:I*(x)≦1/c] where I*(x) = ∫01I(x′(t))dt and I is Cramér's rate function. © 1994 Springer-Verlag.

#### Volume

98

#### Issue

1

#### First Page

1

#### Last Page

5

#### DOI

10.1007/BF01311345

#### ISSN

01788051

#### E-ISSN

14322064

#### Recommended Citation

Sanchis, Gabriela R., "A functional limit theorem for Erdös and Rényi's law of large numbers" (1994). *Faculty Publications*. 1536.

https://jayscholar.etown.edu/facpubharvest/1536