Improved limit on the rate of the decay K+ --> pi(+)&mgr;(+)e(-)

We report results of a search for the lepton-family number violating decay K+-->pi(+)&mgr;(+)e(-) from data collected by experiment E865 in 1996 at the Alternating Gradient Synchroton of Brookhaven National Laboratory. We place an upper limit on the branching ratio at 3.9x10(-11) ( 90% C.L.). Together with results based on data collected in 1995 and an earlier experiment, E777, this result establishes a combined 90% confidence level upper limit on the branching ratio at 2.8x10(-11). We also report a new upper limit on the branching ratio for pi(0)-->&mgr;(+)e(-) of 3.8x10(-10) ( 90% C. L.).