Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals

The problem of restoration of an element $f$ of Euclidean functional space $L^2( X )$ based on the results of meas-urements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension for which the projections of element f to them allow estimates with a given accuracy, is received. The effective rank $\rho(\delta)$ of the estimation problem is defined as the function equal to the maximum dimension of an orthogonal component $Pf$ of the element $f$ which can be estimated with a error, which is not surpassed the value $\delta$. The example of restoration of a spectrum of radiation based on a finite set of experimental data is given.