Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernoulli Randomness and Biased Normality   One can consider $\mu$-Martin-L\"of randomness for a probability measure
$\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0,
1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters
$p_0, p_1, \dotsc, p_{n-1}$, and we introduce a biased version of normality. We
prove that every Bernoulli random real is normal in the biased sense, and this
has the corollary that the set of biased normal reals has full Bernoulli
measure in $n^{\omega}$. We give an algorithm for computing biased normal
sequences from normal sequences, so that we can give explicit examples of
biased normal reals. We investigate an application of randomness to iterated
function systems. Finally, we list a few further questions relating to
Bernoulli randomness and biased normality.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess