[math] \newcommand{\mathds}{\mathbb}[/math]

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Clarify all the details for the standard cube of measures

[[math]] \xymatrix@R=16pt@C=18pt{ &\mathfrak B_t\ar@{-}[rr]\ar@{-}[dd]&&\Gamma_t\ar@{-}[dd]\\ \beta_t\ar@{-}[rr]\ar@{-}[dd]\ar@{-}[ur]&&\gamma_t\ar@{-}[dd]\ar@{-}[ur]\\ &B_t\ar@{-}[rr]\ar@{-}[uu]&&G_t\ar@{.}[uu]\\ b_t\ar@{-}[uu]\ar@{-}[ur]\ar@{-}[rr]&&g_t\ar@{-}[uu]\ar@{-}[ur] } [[/math]]

by proving that we have indeed the Bercovici-Pata bijection on the vertical.