an:01564409
Zbl 0971.60034
Khrennikov, A. Yu.
The Bernoulli theorem for probabilities that take \(p\)-adic values
EN
Dokl. Math. 55, No. 3, 402-405 (1997); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 354, No. 4, 461-464 (1997).
00042397
1997
j
60F99 11K41 60A99
Bernoulli scheme; \(p\)-adic probability; \(p\)-adic characteristic function
The author considers the sequence of normalized sums
\[
T_n=\tfrac{1}n(\xi_1+\cdots +\xi_n),\quad n=1,2,\ldots ,
\]
where \(\xi_1,\ldots ,\xi_n,\ldots\) are independent random variables taking values 0 and 1 with probability 1/2. The probability is understood as a \(\mathbb Q_p\)-valued bounded measure. It is shown that if a sequence \(\{n_k\}\) converges in a \(p\)-adic metric, then the subsequence \(\{T_{n_k}\}\) of the normalized sums converges in a certain weak sense. For a more detailed exposition see the author's book ``Non-Archimedean analysis: Quantum paradoxes, dynamical systems and biological models'' (1997; Zbl 0920.11087).
Anatoly N.Kochubei (Ky??v)
Zbl 0920.11087