# pr.likelihood – Random Fourier succession in Hilbert house Answer

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## pr.likelihood – Random Fourier succession in Hilbert house

Let $$H$$ breathe a Hilbert house, and $$X_n$$,
$$nin mathbb {Z}$$, breathe a sequence of impartial Bernoulli random variables
$$P(X_n = pm 1) = frac 12$$. Is there a characterization of the sequences
$$a_n$$, $$nin mathbb{Z}$$, in $$H$$ such that the succession
$$sum_n a_n X_n e^{int}, quad t in [0,2pi],$$
is sort of certainly uniformly convergent in $$H$$?

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