XIII: 01, 1-3, LNM 721 (1979)
BORELL, Christer
On the integrability of Banach space valued Walsh polynomials (Banach space valued random variables)
The $L^2$ space over the standard Bernoulli measure on $\{-1,1\}^N$ has a well-known orthogonal basis $(e_\alpha)$ indexed by the finite subsets of $N$. The Walsh polynomials of order $d$ with values in a Banach space $E$ are linear combinations $\sum_\alpha c_\alpha e_\alpha$ where $c_\alpha\in E$ and $\alpha$ is a finite subset with $d$ elements. It is shown that on this space (as on the Wiener chaos spaces) all $L^p$ norms are equivalent with precise bounds, for $1<p<\infty$. The proof uses the discrete version of hypercontractivity
Keywords: Walsh polynomials, Hypercontractivity
Nature: Original
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XIII: 02, 4-21, LNM 721 (1979)
CHATTERJI, Shrishti Dhav
Le principe des sous-suites dans les espaces de Banach (Banach space valued random variables)
The ``principle of subsequences'' investigated in the author's paper 604 says roughly that any suitably bounded sequence of r.v.'s contains a subsequence which in some respect ``looks like'' a sequence of i.i.d. random variables. Extensions are considered here in the case of Banach space valued random variables. The paper has the character of a preliminary investigation, though several non-trivial results are indicated (one of them in the Hilbert space case)
Keywords: Subsequences
Nature: Original
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XIII: 03, 22-40, LNM 721 (1979)
GINÉ, Evarist
Domains of attraction in Banach spaces (Banach space valued random variables)
To be completed
Comment: A correction is given as 1402
Nature: Original
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XIII: 04, 41-71, LNM 721 (1979)
LAPRESTÉ, Jean-Thierry
Charges, poids et mesures de Lévy dans les espaces vectoriels localement convexes (Banach space valued random variables)
To be completed
Nature: Original
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XIII: 05, 72-89, LNM 721 (1979)
MARCUS, Michael B.; PISIER, Gilles
Random Fourier series on locally compact abelian groups (Banach space valued random variables, Harmonic analysis)
To be completed
Nature: Original
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XV: 03, 11-37, LNM 850 (1981)
LEDOUX, Michel
La loi du logarithme itéré bornée dans les espaces de Banach (Banach space valued random variables)
To be completed
Keywords: Law of the iterated logarithm
Nature: Original
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