We present the results of a large scale search for new members of the Pleiades star cluster using 2MASS near-infrared photometry and proper motions derived from POSS plates digitized by the USNO PMM program. The search extends to a 10 degree radius around the cluster, well beyond the presumed tidal radius, to a limiting magnitude of R ~ 20, corresponding to ~ 0.07 M_sun at the distance and age of the Pleiades. Multi-object spectroscopy for 528 candidates verifies that the search was extremely effective at detecting cluster stars in the 1 - 0.1 M_sun mass range using the distribution of H_alpha emission strengths as an estimate of sample contamination by field stars. When combined with previously identified, higher mass stars, this search provides a sensitive measurement of the stellar mass function and dynamical structure of the Pleiades. The degree of tidal elongation of the halo agrees well with current N body simulation results. Tidal truncation affects masses below ~ 1 M_sun. The cluster contains a total mass ~ 800 M_sun. Evidence for a flatter mass function in the core than in the halo indicates the depletion of stars in the core with mass less than ~ 0.5 M_sun, relative to stars with mass ~1 - 0.5 M_sun, and implies a preference for very low mass objects to populate the halo or escape. The overall mass function is best fitted with a lognormal form that becomes flat at ~ 0.1 M_sun. Whether sufficient dynamical evaporation has occurred to detectably flatten the initial mass function, via preferential escape of very low mass stars and brown dwarfs, is undetermined, pending better membership information for stars at large radial distances.
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