Abstract
Let E be a Banach space and Π: E→ℝ+ be symmetric, continuous and convex. Let {Ui} and {ri} be independent sequences of random variables having, respectively, U(0, 1) and symmetric Bernoulli distributions, and let {Ui(j)} and {ri(j)} for j=1, 2, ..., d be independent copies of these sequences. We prove two-sided inequalities between the quantities {Mathematical expression} and their "decoupled" versions {Mathematical expression}, for Bochner integrable Fi: [0, 1]d→E. This generalizes results of Kwapień and of Zinn.
Original language | English (US) |
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Pages (from-to) | 499-507 |
Number of pages | 9 |
Journal | Probability Theory and Related Fields |
Volume | 75 |
Issue number | 4 |
DOIs | |
State | Published - Aug 1987 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty