## Annals of Probability

### Some Tauberian Theorems Related to Coin Tossing

#### Abstract

Let $A$ be a subset of the integers and let $S_n$ be the number of heads in $n$ tosses of a $p$ coin. If $\lim_{n\rightarrow\infty} P(S_n \in A)$ exists for some $p$ then the limit exists for all $p$ and does not depend on $p$. The relation of the limit to the density of $A$ and to a similar Poisson limit is also given.

#### Article information

Source
Ann. Probab., Volume 6, Number 3 (1978), 483-490.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995532

Digital Object Identifier
doi:10.1214/aop/1176995532

Mathematical Reviews number (MathSciNet)
MR474449

Zentralblatt MATH identifier
0396.10044

JSTOR