Sentence examples for singular measure from inspiring English sources

In fact the correct interpretation of Δf2 is as a singular measure, a result due to Kusuoka; we give a new proof of this fact.

These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure.

From [1] we know that σ ⊆ ∂ D is the smallest closed set such that θ is analytic across ∂ D ∖ σ , and σ consists of the accumulation points of zeros of θ and the closed support of the associated singular measure.

end{aligned}It is well known that the support of the singular measure (sigma =sigma _f) satisfies begin{aligned} mathop {mathrm {supp}}nolimits sigma _fsubset mathfrak {S}_0(f)={zin {mathbb {T}}: f z)=0}, end{aligned} (6.3)see for example, Hoffman [20], p.

It implies that either the decay at infinity is false, although not probable, implying that the time evolution of probability densities ceases to be tight, or the function N ( t ) may become a singular measure in finite time instead of being an L loc 1 ( R + ) function.

We address (but do not fully answer) the question: For which B can one find a (convergent) sequence { fn}n=1∞ in KB such that the sequence of real measures {log | fn|dθ}n=1∞ converges weak-star to some nontrivial singular measure on ∂D?

And in the rare cases where colleges do delay, the administration is supposed to take singular measures to make sure the accuser is comfortable remaining on campus.

It means that the weak limit of q ε 2 does not contain singular measures.

Uniform L2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimension.

Probabilistic Support Vector Machines and Dominant Singular Measures are used to segment the road regions, and multistage post- processing is done to remove non-road parts.

A measure μ is said to be Lp-improving if μ ∗ Lp ⊂ Lq for some q > p. It is known that certain singular measures supported on curves in R2 are Lp-improving.