A lemma of Arcones. Its more detailed proof.
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Series of problems in Probability Theory
Here the formulation and a more detailed explanation of the proof
of Lemma 1 in Arcones' paper Limit theoremss for non-linear functionals
of a stationary Gaussian sequence of vectors (The Annals of Probability
1994 Vol. 22 No.~4, 2242--2274) is given. This lemma is useful when
limit theorems for non-linear functionals of vector-valued Gaussian
random fields are investigated. This note also discusses the role of
this result in the study of certain problems.
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