This paper deais with the model, wherex(t,s) denotes a known integrable function,. The problem is to estimate the unknown function β(s. We give a CAUSS-MARKOV estimator and its normal equation. In addition we investigate under what conditions the resulting G-M estimator remains invariant whenϵtis replaced by. Furthermore we give under certain additional information about βswhich can be used to obtain a better estimator for βsthan the G-M estimator is. We consider the following informations:is contained in a proper subspace of the setThe finite dimensional regression model represents a special case of the modell under consideration. As an application of the results we also give an example from the variance analysis.