ON THE FORMULATION OF UNIFORM LAWS OF LARGE NUMBERS - A TRUNCATION APPROACH

The paper develops a general framework for the formulation of generic uniform laws of large numbers. In particular, we introduce a basic gen eric uniform law of large numbers that contains recent uniform laws of large numbers by Andrews [2] and Hoadley [9] as special cases. We als o develop a truncation approach that makes it possible to obtain unifo rm laws of large numbers for the functions under consideration from un iform laws of large numbers for truncated versions of those functions. The point of the truncation approach is that uniform laws of large nu mbers for the truncated versions are typically easier to obtain. By co mbining the basic uniform law of large numbers and the truncation appr oach we also derive generalizations of recent uniform laws of large nu mbers introduced in Potscher and Prucha [15, 16].