Sentence examples for the underlying measures from inspiring English sources

Still, not all of the underlying measures in the Shop.org study showed progress.

The underlying measures of coal have proved important for the development of the area; it was around Worsley Delph that the settlement first began to grow.

A simple difference is in units of the underlying measures (money, frequency, incidence, area, etc).; some of these units permit direct comparability and others do not.

In the present paper, a simplification is achieved by extending the given operator (a positive L1-contraction) to the class of all (i.e., not necessarily measurable) functions on the underlying measure space.

When the underlying measure is imperfect, marginal improvements from 96%to99%9% may reflect error in measurement and denominator management more than nearly perfectly reliable performance.

The underlying measure of the deficit has been revised down substantially downwards.

If however, the underlying measure is close to 0, the feature becomes irrelevant to the clustering of (x_i).

The covariance of the deficiency, then, is well defined in terms of the underlying measure P on the full probability space.

Especially, in recent years, many classical results concerning the theory of Calderón-Zygmund operators and function spaces have been proved still valid if the underlying measure is a nonnegative Radon measure on R d which only satisfies (1.1) (see [1 8]).

Based on earlier work of the authors in [7], and [8] concerning the boundary behavior of continuous linear maps, the second author and Weizsäcker had shown that a required condition was naturally satisfied when the underlying measure space was second countable.

The classical theory of one-parameter harmonic analysis for maximal functions and singular integrals on ((mathbb{R}^{n}; mu)) has been developed under the assumption that the underlying measure μ satisfies the doubling property, i.e., there exists a constant (C > 0) such that (mu(B(x; 2r)) leq Cmu(B(x; r))) for every (x in mathbb{R}^{n}) and (r > 0).