Many experimentalists were accustomed to think that any independent measurement forms a non-correlated(independent)measurement that depends weakly from others.We are trying to reconsider this conventional point of view and prove that similar(repeated)measurements can form a strongly-correlated sequence of random functions with memory.In other words,successive measurements “remember” each other at least in the vicinity of their nearest neighbors.This observation and justification on real data help to fit the wide set of data based on the Pronys fitting function.The Pronys decomposition follows from the quasi-periodic(QP)properties of the measured functions and includes the Fourier transform as a partial case.This type of data presentation helps to create a new platform for analysis of different strongly correlated data and obtain a specific amplitude-frequency response(AFR)for different random functions analyzed.It contains less number of the fitting parameters in comparison with its number of initial data points.Actually,the calculated AFR can be considered as the generalized Prony spectrum(GPS),which will be extremely useful in cases where the simple model pretending on description of the measured data is absent but vital necessity of their quantitative description is remained.These possibilities open a new way for clusterization of the initial data and additional information that is contained in these data gives an additional possibilites for their detailed analysis.The electron paramagnetic resonance(EPR)measurements realized for empty resonator(pure noise data)and resonator containing a sample(CeO2 in our case)confirmed the existence of the QP processes in reality.But we think that the detection of the QP processes is a common feature of many repeated measurements and this unexpected property of successive measurements should attract an attention of many experimentalists.Especially the GPS will be extremely useful for analysis of complex and different fractal systems,where a simple("best fit")model is absent but there is necessity to express the basic properties of the long-time series data(medical,technical,geophysical,economical and etc.)in terms of some reduced set of quantitative parameters having clear meaning.The preliminary results of application of this approach to other sets of data have been outlined quite recently [1] but new common elements that are appeared in analysis of different data make this decomposition rather general.In future we expect that this GPS approach forced to reconsider the conventional point of view on the process of measurements and a researcher will receive new deterministic information that is contained in routine measurement process.