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These proceedings contain selected papers presented at the Conference on Approximation, Probability and Related Fields held in Santa Barbara, California, on May 20-22, 1993. The main topics of the conference were: 1) approximation of functions by polynomials, splines, and operators, and applications to stochastics 2) numerical methods for approximation of deterministic and stochastic integrals 3) orthogonal polynomials and stochastic processes 4) positive linear operators and related deterministic and stochastic inequalities 5) multivariate approximation and interpolation 6) rate of convergence in probability theory 7) approximations and martingales 8) deterministic and stochastic inequalities 9) stability of deterministic and stochastic models 10) signal analysis 11) prediction theory 12) wavelets and approximations based on wavelets The Conference was very successful and received many compliments. We quote some of the letters sent by the participants: -"Many thanks for the wonderful conference and the exemplary organization!" -"Many thanks for your good and effective work" We would like to thank the international organizing committee consisting of Paul Butzer, Stamatis Cambanis and Zuhair Nashed as well as the local organizing committee consisting of Bessy Athanasopoulos, Raisa Feldman, and Gleb Haynatzki for their superb work and for their contribution to the success of the Conference. The chairmer A ~ C*p,. ~lflIl", George Anastassiou Svetlozar Rachev ix CONTENTS 1. Preservation of Moduli of Continuity for Bernstein-type Operators ...Jose A. Adell and Jesus de la Cal 2. Lp-Korovkin Type Inequalities for Positive Linear Operators ...19 G. A. Anastassiou 3. On Some Shift-Invariant Integral Operators, Multivariate Case ...