The random infinite set (RFS) approach to information fusion addressed target track-labeling from the outset. The first implementations of RFS filters did not do so because of computational concerns, whereas subsequent implementations employed heuristics. The labeled RFS (LRFS) theory of B.-T. Vo and B.-N. Vo was the first systematic, theoretically rigorous formulation of true multitarget tracking; and led to the generalized labeled multi-Bernoulli (GLMB) filter (the first provably Bayes-optimal multitarget tracking algorithm). This paper addresses the feasibility of theoretically rigorous cardinalized probability hypothesis density (CPHD) filters. We show that an approximation of the GLMB filter, known as the LMB filter, can be reinterpreted as a theoretically rigorous labeled PHD (LPHD) filter. We also prove two characterization theorems for the probability generating functionals (p.g.fl's) of LRFS’s.