TY  - JOUR
ID  - Rajba2012
LB  - Rajba2012
AU  - Rajba, Teresa
TI  - An application of the Choquet theorem to the study of randomly-superinvariant measures
ST  - An application of the Choquet theorem to the study of randomly-superinvariant measures
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 2
SP  - 317
EP  - 326
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.2.317
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.2.317
AB  - 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 \(\Theta\).
KW  - backward translation operator
KW  - backward difference operator
KW  - integral inequality
KW  - extreme point
SN  - 1232-9274
ER  -