  Any Riemannian manifold has a canonical collection of valuations (finitely
additive measures) attached to it, known as the intrinsic volumes or
Lipschitz-Killing valuations. They date back to the remarkable discovery of H.
Weyl that the coefficients of the tube volume polynomial are intrinsic
invariants of the metric. As a consequence, the intrinsic volumes behave
naturally under isometric immersions. This phenomenon, subsequently observed in
a number of different geometric settings, is commonly referred to as the Weyl
principle. In general normed spaces, the Holmes-Thompson intrinsic volumes
naturally extend the Euclidean intrinsic volumes. The purpose of this note is
to investigate the applicability of the Weyl principle to Finsler manifolds. We
show that while in general the Weyl principle fails, a weak form of the
principle unexpectedly persists in certain settings.
