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Diffstat (limited to 'proofs.tex')
| -rw-r--r-- | proofs.tex | 15 |
1 files changed, 7 insertions, 8 deletions
@@ -316,14 +316,13 @@ In particular, \begin{gather*} \forall S\subseteq\mathcal{N},\quad A(S)^{-1} \succeq A(S\cup\{i\})^{-1} \end{gather*} -as $A(S)\leq A(S\cup\{i\})$. Observe that - \begin{gather*} - \forall S\subseteq\mathcal{N}\setminus\{i\},\quad - P_{\mathcal{N}\setminus\{i\}}^\lambda(S)\geq - P_{\mathcal{N}\setminus\{i\}}^\lambda(S\cup\{i\}),\\ - \forall S\subseteq\mathcal{N},\quad P_{\mathcal{N}\setminus\{i\}}^\lambda(S) - \geq P_\mathcal{N}^\lambda(S). - \end{gather*} +as $A(S)\preceq A(S\cup\{i\})$. Observe that + % \begin{gather*} + % \forall +$P_{\mathcal{N}\setminus\{i\}}^\lambda(S)\geq P_{\mathcal{N}\setminus\{i\}}^\lambda(S\cup\{i\})$ for all $S\subseteq\mathcal{N}\setminus\{i\}$, and + % ,\\ + $P_{\mathcal{N}\setminus\{i\}}^\lambda(S) \geq P_\mathcal{N}^\lambda(S),$ for all $S\subseteq\mathcal{N}$. + %\end{gather*} Hence, \begin{align*} \partial_i F(\lambda) |