We consider a manifold $M$ with a foliation $F$ given by a locally free actionof a commutative Lie group $H$. Also we assume that there exists an integrable Ehresmann connection on $(M, F)$ invariant with respect to the action of the group $H$. We get the structure of the restriction of the algebra$C_0(M)$ to the leaves in three partial cases. Also we consider aclassification of the quasiinvariant measures and means on the leaves of$F$.
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