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On the best constant in the Khinchin-Kahane inequality. (English) Zbl 0812.60010
Summary: We prove that if \(r_ i\) is the Rademacher system of functions, then \[ \left( \int \left \| \sum^ n_{i=1} x_ i r_ i(t) \right \|^ 2dt \right)^{1/2} \leq \sqrt 2 \int \left \| \sum^ n_{i=1} x_ i r_ i(t) \right \| dt \] for any sequence of vectors \(x_ i\) in any normed linear space \(\mathbb{F}\).

MSC:
60B11 Probability theory on linear topological spaces
46B09 Probabilistic methods in Banach space theory
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