Structure of function algebras on foliated manifolds (Q1422290)

Let \(M\) be a manifold with a foliation \(F\) given by a locally free action of a commutative Lie group \(H\). Assume further that there exists an integrable Ehresmann connection for \(F\) which is invariant with respect to the action of \(H\). Let \(C_0(M)\) denote the algebra of continuous functions on \(M\) that vanish at infinity, and let \(C_0(M)| _L\) denote the restriction of \(C_0(M)\) to a leaf \(L\) of \(F\). The author investigates the structure of \(C_0(M)| _L\) in three special cases and connects this problem to the so-called Radon-Nikodym problem on the leaves of the foliation. In this he considers the classification of the quasi-invariant measures and means on the leaves of \(F\).