Abstract: In this paper, the author extends Ren's results in plane to the case of R_2n,i.e., estimates the kinematic measure of a convex domain D₁ with boundary ∑₁ moving to another domain D₀ with boundary ∑₀ under the isometry group G in R_2n. A sufficient condition for D₀ contain D₁ by using kinematic foundamatal formula and Poincare's formula in R_n is obtained.

Key words: Convex domain, kinematic foundamental formula, Poincare's formula