Opuscula Math. 32, no. 2 (), 317-326
http://dx.doi.org/10.7494/OpMath.2012.32.2.317
Opuscula Mathematica

# An application of the Choquet theorem to the study of randomly-superinvariant measures

Abstract. Given a real valued random variable $$\Theta$$ we consider Borel measures $$\mu$$ on $$\mathcal{B}(\mathbb{R})$$, which satisfy the inequality $$\mu(B) \geq E\mu(B-\Theta)$$ ($$B \in \mathcal{B}(\mathbb{R})$$) (or the integral inequality $$\mu(B) \geq \int_{-\infty}^{+\infty} \mu(B-h)\gamma (dh)$$). We apply the Choquet theorem to obtain an integral representation of measures $$\mu$$ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable $$\Theta$$.
Keywords: backward translation operator, backward difference operator, integral inequality, extreme point.
Mathematics Subject Classification: 60E15, 26D10.
Cite this article as:
Teresa Rajba, An application of the Choquet theorem to the study of randomly-superinvariant measures, Opuscula Math. 32, no. 2 (2012), 317-326, http://dx.doi.org/10.7494/OpMath.2012.32.2.317

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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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