quality:correction
Points are uniformly distributed

If the homogeneous point process is defined on the real line as a mathematical model for occurrences of some phenomenon, then it has the characteristic that the positions of these occurrences or events on the real line (often interpreted as time) will be uniformly distributed. More specifically, if an event occurs (according to this process) in an interval (a, b ] {\displaystyle \textstyle (a,b]} where a ≤ b {\displaystyle \textstyle a\leq b}, then its location will be a uniform random variable defined on that interval. Furthermore, the homogeneous point process is sometimes called the uniform Poisson point process (see Terminology). This uniformity property extends to higher dimensions in the Cartesian coordinate, but not in, for example, polar coordinates.