Sentence examples similar to measurable function considering from inspiring English sources

Given u a measurable function we consider the k-truncation of u defined by T_{k} u)= textstylebegin{cases} u, & |u| leq k, kfrac{u}{|u|}, & |u|>k.

Let E be a Lebesgue-measurable set with (m(E) < infty) and (X = L^{infty}(E)) denote the class of essentially bounded measurable functions on E. Consider the Hilbert space (L^{2}(E)).

Lebesgue measure, measurable functions, integrability, completeness of L-p spaces.

Next, as an application, we consider some geometric properties of φ-means of a real-valued measurable function f on Ω.

To see this, let be an arbitrary measurable function.

Given the values of a measurable function m:Rd→R at n arbitrarily chosen points in Rd the problem of estimating m on whole Rd is considered.

We consider non-local elliptic operators with kernel K y)="a y)/|y|d+σ, where 0<σ<2 is a constant and a is a bounded measurable function.

Similar statements can be made about a measurable function in $\mathbb R^n$.

where is a measurable function.

A function is called N- measurable on if for every measurable function the function is measurable.

(b) defines a measurable function from into.