 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".The Levi-Civita connection of "M" gives rise to a splitting of the tangent bundle
into a vertical space "V" = kerπ* and horizontal space "H" on which π* is a linear isomorphism at each point of UT"M".This splitting induces a metric on UT"M" by declaring that this splitting be an orthogonal direct sum, and defining the metric on "H" by the pullback