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Revision as of 03:00, 7 May 2009
, 03:00, 7 May 2009→Commentary Note 12.5
\prod_{p \in X} (\mathfrak{S}^\mathfrak{L})_{xp}^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\mathfrak{S}^\mathfrak{L})_{xp}^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}})^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}})^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}\mathfrak{W}_p})
\prod_{p \in X} \prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}\mathfrak{W}_p}
</math>
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(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x ~=~
(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{(\mathfrak{L}\mathfrak{W})_q} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{(\mathfrak{L}\mathfrak{W})_q} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p}
\prod_{q \in X} \mathfrak{S}_{xq}^{\sum_{p \in X} \mathfrak{L}_{qp} \mathfrak{W}_p} ~=~
\prod_{q \in X} \prod_{p \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp} \mathfrak{W}_p}
</math>
</math>
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