that of − u by f$_{−}$$_{u}$. Then equation (4) gives Additionally if expectation conditional on z exists, using independence be- tween z and u, then f$_{x}$ = f$_{z}$ ∗ f$_{−}$$_{u}$. (5) w ( z ) = E ( y | z ) = E ( g ( x ) | z ) = ∫ g ( z − u ) f$_{u}$ ( u ) du ; g ∗ f$_{u}$ = w. (6) The system of equations (5 , 6) involves two unknown functions, f$_{u}$ and g, where usually the interest is in the regression function. The regression function could have instead of an observable argument, x, a mismeasured or latent argument, x $^{∗}$. The model could provide more equations if another measurement, x, on x ∗ were available. Consider y = g ( x $^{∗}$) + u$_{y}$ ; (7) x = x ∗ + u$_{x}$ ; (8) z = x ∗ + u. (9) Here x, y, z are observed; assume that u is a Berkson type measurement er- ror independent of z with (unknown) density f, assume that u$_{y}$, u$_{x}$ have zero 6