Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On analogues of C.R.Rao's theorems for locally compact Abelian groups   Let $\xi_1$, $\xi_2$, $\xi_3$ be independent random variables with
nonvanishing characteristic functions, and $a_j$, $b_j$ be real numbers such
that $a_i/b_i\ne a_j/b_j$ for $i\ne j$. Let $L_1=a_1\xi_1+a_2\xi_2+a_3\xi_3$,
$L_2=b_1\xi_1+b_2\xi_2+b_3\xi_3$. By C.R.Rao's theorem the distribution of the
random vector $(L_1, L_2)$ determines the distributions of the random variables
$\xi_j$ up to a change of location. We prove an analogue of this theorem for
independent random variables with values in a locally compact Abelian group. We
also prove an analogue for independent random variables with values in an
$a$-adic solenoid of similar C.R.Rao's theorem. In so doing coefficients of
linear forms are continuous endomorphisms of the group.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: solv-int