Chiral Perturbation Theory (ChPT) [1] has been a successful approach to describing the decays of pseudoscalar mesons. In the ChPT program radiative kaon decays can serve both as an important test and a source of input parameters for the theory. While the decay modes K + → e + νγ (K e2γ ) and µ + νγ (K µ2γ ) have allowed some study of the form factors involved [2,3,4], the decays) allow a more detailed investigation into the structure of these decays. We report here on such an investigation from Experiment 865 at the Brookhaven National Laboratory AGS with a 100-fold increase in the number of events in the former mode and 150-fold increase in the latter [5].The K e2ee and K µ2ee decays are assumed to proceed via exchange of a W + -boson (l + ν) and photon (e + e − ). The decay amplitude [6,7] includes inner bremsstrahlung (IB) corresponding to the tree diagrams in Fig. 1a,b, and structure dependent (SD) radiation (Fig. 1c) parameterized by vector F V , axial F A and R form factors. K e2γ and K µ2γ experiments were actually sensitive only to |F V + F A |. R, which contributes only to decays with an e + e − -pair, has not yet been measured. Inner bremsstrahlung is unambiguously predicted by the K → lν amplitude and is proportional to the kaon decay constant F K = 160 MeV. We included the kaon electromagnetic form factor in Fig. 1b (amplitude A 4 of

A search for lepton flavor violating decays, K+ --> mu+ mu+ pi-, K+ --> e+ e+ pi-, K+ --> pi+ e+ mu-, K+ --> mu+ e+ pi-, and pi0 --> e+ mu-, was performed using the data collected in Experiment E865 at the Brookhaven Alternating Gradient Synchrotron. No signal was found in any of the decay modes. At the 90% confidence level, the branching ratios are less than 3.0x10(-9), 6.4x10(-10), 5. 2x10(-10), 5.0x10(-10), and 3.4x10(-9), respectively.