class of computable probability mass functions of given maximal Kolmogorov complexity , the complexity of P upper bounded by , is given by the MDL function or constrained MDL estimator: where is the total length of two-part code of x with help of model P. Main property It is proved that at each level of complexity the MDL function allows us to select the best model P for the individual string x within a strip of with certainty, not with great probability. Extension to rate distortion and denoising It turns out that the approach can be extended to a theory of rate distortion of individual finite sequences and denoising of individual finite sequences using Kolmogorov complexity. Experiments using real compressor programs have been carried out with success. Here the assumption is that for natural data the Kolmogorov complexity is not far from the length of a compressed version using a good compressor. References Literature , Especially pp. 401–431 about the Kolmogorov structure function, and pp. 613–629 about rate distortion and denoising of individual sequences. Algorithmic information theory