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The notion of the metric measure foliation is introduced by Galaz-Garc\'ia,Kell, Mondino, and Sosa. They studied the relation between a metric measurespace with a metric measure foliation and its quotient space. They showed thatthe curvature-dimension condition and the Cheeger energy functional preservefrom a such space to its quotient space. Via the metric measure foliation, weinvestigate the convergence theory for a sequence of metric measure spaceswhose dimensions are unbounded.

Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation