相关论文: Remarks on the existence of measurable selectors

We find the origin of the integration theory for multifunctions in the sixties in the pioneering works of G. Debreu and R. Aumann, Nobel prizes for the Economy in 1983 and in 2005, respectively. The Aumann integral is defined by means the…

We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

We show the existence of a measurable selector in Carpenter's Theorem due to Kadison. This solves a problem posed by Jasper and the first author. As an application we obtain a characterization of all possible spectral functions of…

In the paper we investigate Borel classes of multivalued functions of two variables. In particular we generalize a result of Marczewski and Ryll-Nardzewski concerning of real function whose ones of its sections are right-continuous and…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…

In this article we prove a generalization of the Beurling--Malliavin Majorant Theorem. In more detail, we establish a new sufficient condition for a function to be a Beurling--Malliavin Majorant. Our result is strictly more general than…

An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…

We prove a Ryll-Nardzewski Theorem for quantum stochastic processes, that shows that under natural assumptions which generalize the classical probability setting, the distributional symmetries of exchangeability and spredability are the…

The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…

If $f : X\mapsto Y$ is a function having Baire property from a metric space $X$ into a separable metric space $Y$ , then $f$ is continuous except on a set of first category. Kuratowski asked whether the condition of separability could be…

When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

We suggest the necessary/sufficient criteria for the existence of a (order-by-order) solution y(x) of a functional equation F(x,y)=0 over a ring. In full generality, the criteria hold in the category of filtered groups, this includes the…

In this paper, the concept of Musielak N-functions and Musielak-Orlicz spaces generated by them well be introduced. Facts and results of the measure theory will be applied to consider properties, calculus and basic approximation of Musielak…

A classical theorem of Kuratowski says that every Baire one function on a G_\delta subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer…

A classical theorem of Menshov states that every measurable function can redefined on a set of arbitrarily small Lebesgue measure, so that the resulting function has uniformly convergent Fourier series. We prove that the same is true if we…

We derive the probabilities of measurement results from Schroedinger's equation plus a definition of macroscopic as a particular kind of thermodynamic limit. Bohr's insight that a measurement apparatus must be classical in nature and…