  We define and study the degeneration property for BV-infinity algebras and
show that it implies that the underlying L-infinity algebras are homotopy
abelian. The proof is based on a generalisation of the well-known identity
\Delta(e^x)=e^x(\Delta(x)+[x,x]/2) which holds in all BV algebras. As an
application we show that the higher Koszul brackets on the cohomology of a
manifold supplied with a generalised Poisson structure all vanish.
