mass points, or for fractal measures). For the equations considered here, when identification and well-posedness holds consistent estimation of the known functions can provide consistent plug-in estimators for the solutions as long as the estimators all be in the classes over which well-posedness obtains. The fact that well-posedness implies consistency of some plug-in estima- tors holds generally. Denote (generically) the known functions by w$_{1}$, ...w$_{M}$, their consistent in topology of S ∗ estimators by ˆ w$_{i}$ ; denote the solutions by g$_{1}$, ..., g$_{K}$ and the plug-in estimators from solving the equations using ˆ w$_{i}$ by ˆ g$_{j}$. If the estimators, ˆ w$_{i}$, are in classes where well-posedness holds, then for any set of ( ψ$_{1}$, ...ψ$_{v}$ ) from S and any neighborhood N$_{vK}$ (0) of zero in real or complex vK − dimensional Euclidean space there is a neighbor- hood of zero, ˜ N$_{vM}$ (0) in the corresponding vM − dimensional space such that event E$_{w}$ = { (( ˆ w$_{1}$, ψ$_{1}$ ) , ..., ( ˆ w$_{1}$, ψ$_{v}$ ) , ( ˆ w$_{2}$, ψ$_{1}$ ) , ..., ( ˆ w$_{M}$, ψ$_{v}$ )) ′ ∈ ˜ N$_{vM}$ (0) } by well-posedness implies the event Consistency of ˆ w$_{i}$ as n → ∞ means that for large enough n probability of E$_{w}$ can be arbitrarily close to 1, thus probability of E$_{g}$ is as close or closer to 1. Thus the condition for consistent plug-in estimation is that the estimators are in the classes of generalized functions that provide well-posedness of solutions with probability approaching 1. E$_{g}$ = { ((ˆ g$_{1}$, ψ$_{1}$ ) , ..., (ˆ g$_{1}$, ψ$_{v}$ ) , (ˆ g$_{2}$, ψ$_{1}$ ) , ..., (ˆ g$_{K}$, ψ$_{v}$ )) ′ ∈ N$_{vK}$ (0) } . 49