Continuous models of percolation theory. I

Percolation models in which defect centers are distributed randomly in space in accordance with Poisson's law and the shape of each defect is also random are considered. Coincidence of two critical points is proved. One of these corresponds to the time when the mean number of defects connected to a given defect becomes infinite. The other corresponds to the existence of percolation in an arbitrarily large region of space.