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