Extending the FCLT version of L=λWL=λW

The functional central limit theorem (FCLT) version of Little’s law (L=λWL=λW) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in the system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exploiting monotonicity.