Sentence examples for classes of measures from inspiring English sources
In particular, we identify large classes of measures for which the corresponding convolution operators have excellent spectral properties.
We revise in this subsection three classes of measures, defined on the attractor, that capture three distinct structural aspects of the attractor: geometric, spacial distribution, spacial correlation.
We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on Rn and different classes of measures: Gaussian measures on Rn, symmetric Bernoulli and symmetric uniform probability measures on R, as well as their convolutions.
In particular, we have singled out two different classes of measures, namely classical and parametric entropy measures defined on graphs, and have examined their interrelations.
We also prove quadratic upper bounds on a class of measures that are not necessarily convex.
Let us present now the class of measures that we use in the definition of Sobolev space.
This defect of the quadratic class of measures corresponds to a problem familiar from the investigation of attempts to capture truthlikeness simply in terms of classes of true and false consequences, or in terms of truth value and content alone.
259 (3) (2010) 731 779], Naor and Tao introduce a new class of measures with a so-called micro-doubling property and present, via martingale theory and probability methods, a localization theorem for the associated maximal functions.
The first class of measures takes into account the number of formulae required to produce an inconsistency: the more formulae required to produce an inconsistency, the less inconsistent the base.
