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Konstantinos Makantasis edited untitled.tex
over 8 years ago
Commit id: a663911943c710664686eafd09c702d19c7c4691
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index 28864b7..32cdc5f 100644
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Using (\ref{eq:cons_AtakesPlace}) and (\ref{eq:cons_eventA}) the inequalities
\begin{equation}
\label{eq:cons_AleqTk}
\inf_{a \in \Lambda(\beta_k)} \int Q(z,a)dF(z) + \frac{\epsilon}{2} > \int Q(z,a^*)dF(z) > \frac{1}{l}\sum_{i=1}^{l}Q(z_i. a^*) +
\espilon \epsilon > \inf_{a \in \Lambda(\beta_k)} \frac{1}{l} \sum_{i=1}^{l} Q(z_i, a) + \epsilon
\end{equation}
hold and implie that event $T_k$ aldo takes place. This means that
\begin{equation}
A \subseteq T_k \subseteq T \Longrightarrow P(A) \leq P(T_k) \leq P(T) \xrightarrow[l \rightarrow \infty]{} 0 .
\end{equation}