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On Geary’s theorem for the field of p-adic numbers


Let ℚ p , where p > 2, be a field of p-adic numbers. We consider two independent identically distributed random variables with values in ℚ p and distribution μ with a continuous density. We prove that the sum and the squared difference of these random variables are independent if and only if μ is an idempotent distribution, i.e., a shift of the Haar distribution of a compact subgroup of the additive group of the field ℚ p .

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Correspondence to M. V. Myronyuk.

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Original Russian Text © M.V. Myronyuk, G.M. Feldman, 2016, published in Doklady Akademii Nauk, 2016, Vol. 467, No. 2, pp. 131–134.

The article was translated by the authors.

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Myronyuk, M.V., Feldman, G.M. On Geary’s theorem for the field of p-adic numbers. Dokl. Math. 93, 152–154 (2016).

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  • Haar Measure
  • DOKLADY Mathematic
  • Compact Subgroup
  • Compact Abelian Group
  • Continuous Density