An integral for nonmeasurable correspondences and the shapley-interval.
An integral formula for entropy of doubly stochastic operators
A new formula for entropy of doubly stochastic operators is presented. It is also checked that this formula fulfills the axioms of the axiomatic definition of operator entropy, introduced in an earlier paper of Downarowicz and Frej. As an application of the formula the 'product rule' is obtained, i.e. it is shown that the entropy of a product is the sum of the entropies of the factors. Finally, the proof of continuity of the new 'static' entropy as a function of the measure is given.
An Integral in Topological Spaces II.
An integral operator inequality with applications.
An integral related to the Cauchy transform on the Sierpiński gasket.
An integral representation for decomposable measures of measurable functions. (Summary).
An integral representation for decomposable measures of measurable functions.
An intersection property of sets with positive measure
An invariant for continuous mappings
An isoperimetric inequality in R3
An isoperimetric inequality on the ℓp balls
The normalised volume measure on the ℓnp unit ball (1≤p≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pãlog1−1/p(1/ã), where ã=min(a, 1−a).
An L...-Estimate for the gradient of extremals.
An Open Mapping Theorem for Measures.
An uncountable partition contained in the atomless σ-field
This short note considers the question of whether every atomless σ-field contains an uncountable partition. The paper comments the situation for a couple of known σ-fields. A negative answer to the question is the main result.
Analyse des correspondances et codage par une probabilité de transition
Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
Analytic capacity and linear measure
Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space
In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.
Analytic gaps
We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.
Analytic joint spectral radius in a solvable Lie algebra of operators
We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.