Random LSC Functions: An Ergodic Theorem
Lisa A. Korf, Roger J.‐B. Wets · Mathematics of Operations Research · 2001
An ergodic theorem for random lsc (lower semicontinuous) functions is obtained by relying on a “scalarization” of such functions. In the process, Kolmogorov's extension theorem for random lsc functions is established. Applications to statistical estimation problems, composite materials, and stochastic optimization problems are briefly noted.