Sentence examples similar to measurable function throughout from inspiring English sources

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

(b) defines a measurable function from into.

Throughout the paper, we denote by, I and f a probability space, an interval of ℝ and a real-valued measurable function on Ω with f ∈ I for almost all ω ∈ Ω, respectively.

Therefore (4.2) is a measurable function as a linear combination of measurable ones.

Let f be a measurable function on R n.

where f is a nonnegative measurable function on R n.

Let and let be a nonnegative measurable function on.

Let g be a measurable function on (mathbb {R}^{n}).

Let f be a measurable function on (Bbb {R}^{n}).

If u is a measurable function on ∂ C n satisfying.

If φ ∈ H, then ∥ φ ∥ H = ( ∫ | ∇ φ | 2 d x + ∫ V ( x ) | φ | 2 d x ) 1 2. (7) Throughout this paper, we make the following assumptions on V ( x ) : { inf x ∈ R n V ( x ) = V ¯ ( x ) > 0, V ( x )  is a  C 1  bounded measurable function on  R n, lim x → ∞ V ( x ) = ∞.