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Lisa
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Сoincidence of discrete random variables

Let $\xi, \eta$ be a discrete random values and $\mathbb E| ξ |$, $\mathbb E | η |$ < $+\infty$, and any value of these values ​​are accepted with a non-zero probability. How to prove that from $\mathbb E (ξ | η) ≥ η$, $\mathbb E (η | ξ) ≥ ξ$ follows $ξ = η$?

Lisa
  • 113
  • 4