A nonstandard combinatorial technique for integral equations

In ref. [1] it is shown that the Mobius-Rota inversion can be generalized to any locallystandard infinite poset S in the nonstandard sense. The result is as follows. Let C be a locally*-finite poset with a 0-element O. Suppose that *μ1∈*I（C,*K）. a *-incidence algebra of C,over a field *K of characteristic O. possesses an inverse *μ2=*μ1-1,where *μ1, *μ2 are*-Mobius operators. Then for *f, *g∈Map （C. *K）, the functions from C into *K,