The award of the 1999 Nobel Prize for physics to G. 't Hooft and M. Veltman, and the success of the predictions of their formulation ͓1͔ of the renormalized non-Abelian quantum loop corrections for the standard model ͓2͔ of the electroweak interactions in confrontation with data of CERN e ϩ e Ϫ collider LEP experiments, underscores the need to continue to test this theory at the quantum loop level in the gauge boson sector itself. This emphasizes the importance of the on-going precision studies of the processes e ϩ e Ϫ →W ϩ W Ϫ ϩn(␥)→4 f ϩn(␥) at LEP2 energies ͓3-5͔, as well as the importance of the planned future higher energy studies of such processes in linear collider ͑LC͒ physics programs ͓6-9͔. We need to stress that hadron colliders also have considerable reach into this physics and we hope to come back to their roles elsewhere ͓10͔.In what follows, we present precision predictions for the event selections ͑ES͒ of the LEP2 Monte Carlo ͑MC͒ Workshop ͓11͔, for the processesfinalstate radiation ͑FSR͒ leading-pole approximation ͑LPA͒ formulation, as it is realized in the MC program YFSWW3-1.14 ͓12,13͔, in combination with our all four-fermion processes MC event generator KORALW-1.42 ͓14,15͔ so that the respective four-fermion background processes are taken into account in a gauge-invariant way. Indeed, gauge invariance is a crucial aspect of our work and we stress that we maintain it throughout our calculations.Recently, the authors in Refs. ͓16͔ have also presented MC program results for the processes e ϩ e Ϫ →W ϩ W Ϫ ϩn(␥)→4 f ϩn(␥), nϭ0,1, in combination with the complete background processes that feature the exact LPA O(␣) correction. Thus, we will compare our results, where possible, with those in Refs. ͓16͔ in an effort to check the overall precision of our work. As we argue below, the two sets of results should agree at a level below 0.5% on observables such as the total cross section.More specifically, in YFSWW3-1.13 ͓13͔, the leading-pole approximation ͑LPA͒ is used to develop a fully gaugeinvariant YFS-exponentiated calculation of the signal process e ϩ e Ϫ →W ϩ W Ϫ ϩn(␥)→4 f ϩn(␥), which features the exact O(␣) electroweak correction to the production process and the O(␣ 2 ) LL corrections to the final-state decay processes. The issue is how to combine this calculation with that of in Refs. ͓14,15͔, for the corresponding complete Born-level cross section with YFS-exponentiated initial-state O(␣ 3 ) LL corrections. In this connection, we point out that the LPA enjoys some freedom in its actual realization, just as does the LL approximation in the precise definition of the big logarithm L, without spoiling its gauge invariance. This can already be seen from the book of Eden et al. ͓17͔, wherein it is stressed that the analyticity of the S matrix applies to the scalar form factors themselves in an invariant Feynman amplitude, without any reference to the respective external wave functions and kinematical ͑spinor͒ covariants. The classic example illustrated in Ref. ͓17͔ is that of pion-nucleon scatter...
