Supports of Measure Solutions for Spatially Homogeneous Boltzmann Equations

We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in ℝ³ relative to the measure solution.