Sentence examples for measure with finite from inspiring English sources

A DOD is a probability measure with finite support on SO(3), the special orthogonal group in three dimensions.

In the following, μ will always denote a Borel measure with finite total mass, which is initially defined on a certain open subset Ω ⊂ R n.

We also extend this result to a probability absolutely continuous but not necessarily equivalent to the Wiener measure, with finite entropy.

Here we are still assuming that μ is a Borel measure with finite mass, but we could assume that μ ∈ C ∞ as well, stating the same results involving only the total variation of μ, considered as a measure.

Convex optimisation, based on a quadrature approximation of the IMSE criterion and a discretisation of the design space, yields an optimal design in the form of a probability measure with finite support.

(Truncated Riesz potentials) Let μ be Borel measure with finite total mass on R n ; the (truncated) Riesz potential is defined by I β μ ( x, R ) : = ∫ 0 R | μ | ( B ( x, ϱ ) ) ϱ n - β d ϱ ϱ, β > 0, whenever x ∈ R n and 0 < R ≤ ∞.

The infinite convolution of probability measures with finite support and equal distributionμ{pn},{dn}:= δp1−1{0,d1}⁎δ(p1p2)−1{0,d2}⁎⋯ is a Borel probability measure (Cantor Moran measure).

The dual of (C_{0}(mathbb{R}^{N})) can be identified with the space (mathcal {M}(mathbb{R}^{N})) of signed Radon measures with finite mass via the pairing begin{aligned} langlemu,frangle=int_{mathbb{R}^{N}}f,dmu.

To guide the fabrication of the planarized apertures, the illumination profile of the transmitted excitation light was measured computationally with finite element analysis.

The technique developed in this study for estimating the mean sarcomere length uses a number of novel approaches. 1) From the inherit reality of measuring signals with finite length, the underlying mathematical theory for the sarcomere length estimation technique considers functions on finite interval and proposes an unbiased measure of similarities for a pair of functions.

In addition, we review the recent literature on development of adaptive importance sampling techniques to quickly estimate common performance measures associated with finite-state Markov chains.