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Acta Mathematica Hungarica
Authors: Z. Kobayashi, T. Kuzumaki, T. Okada, T. Sekiguchi, and Y. Shiota

Abstract  

We define a probability measure which has Markov property on the unit interval, compute a higher order partial derivative of its distribution function about the parameter. As application, we obtain explicit formulas of a digital sum of the block of the binary number.

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Measures , Wiley, New York, 1968. Billingsley P. Convergence of Probability Measures 1968

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Abstract  

In this paper we study the relaxation of optimal control problems monitored by subdifferential evolution inclusions. First under appropriate convexity conditions, we establish an existence result. Then we introduce the relaxed problem and show that it always has a solution under fairly general hypotheses on the data. Subsequently we examine when the relaxation is admissible. So we show that every relaxed trajectory can be approximated by extremal original ones (i.e. original trajectories generated by bang-bang controls) and that the values of the original and relaxed problems are equal. Some examples are also presented.

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Abstract

The inclusion-exclusion principle is one of the basic theorems in combinatorics. In this paper the inclusion-exclusion principle for IF-sets on generalized probability measures is studied. The basic theorems are proved.

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Abstract  

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the modern probability theory. Results from Kolmogorov [11], Bochner [2], Choksi [6], Metivier [15], Bourbaki [4], Mallory and Sion [12] among others have paved the way of the deep understanding of this problem. All the above results, however, call for some topological concepts, or at least the ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sufficient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

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