Radiative corrections to Kl3 decays

We present a complete calculation of the K-l3 decays K+ --> pi(0)l(+)v(l) and K-0 -->pi(-)l(+)v(l) to O(p(4) (m(d) (-) m(u))p(2), e(2)p(2)) in chiral perturbation theory with virtual photons and leptons. We introduce the concept of generalized form factors and kinematical densities in the presence of electromagnetism, and propose a possible treatment of the real photon emission in K-l3(+) decays. We illustrate our results by applying them to the extraction of the Kobayashi-Maskawa matrix element \V-us\ from the experimental K-l3(+) decay parameters.