 Geometrically, the associated distribution of hyperplanes at the point "u" ∈ UT"x""M" is the inverse image under π* of the tangent hyperplane to the unit sphere in T"x""M" at "u".The volume form θ∧"d"θ"n"−1 defines a measure on "M", known as the kinematic measure, or Liouville measure, that is invariant under the geodesic flow of "M".As a Radon measure, the kinematic measure μ is defined on compactly supported continuous functions "ƒ" on UT"M" by
where d"V" is the volume element on "M", and μ"p" is the standard rotationally-invariant Borel measure on the Euclidean sphere UT"p""M".