Sentence examples for function measurable on from inspiring English sources

where is an real matrix, and is an -dimensional real column vector, with components in the space (where ) of functions integrable on with the degree ; the delay is a function measurable on ; is a given vector function with components in.

By L 0 we denote the class of all functions measurable on with respect to Lebesgue measure.

Let (p: [-pi,pi ]to [1,+infty )) be some Lebesgue measurable function. By (mathrm{L}_{0} ) denote the class of all functions measurable on ([-pi,pi ]) (with respect to Lebesgue measure).

Let (p: [-pi,pi ]to [1,+infty )) be some Lebesgue measurable function. Denote the class of all functions measurable on ([-pi,pi ]) (with respect to the Lebesgue measure) by ({mathscr {L}}_{0} ).

Let f be a real-valued nonnegative function and measurable on E. Then ( ess inf x ∈ E f ( x ) ) − 1 = ess sup x ∈ E 1 f ( x ).

the spaces of complex-valued functions f, measurable on such that: the topological dual space of.

the spaces of complex-valued functions f, measurable on such that: and.

First, we show that the function is -almost measurable on.

A real-valued function, positive and measurable on for some, is said to be slowly varying if (1.3).

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

Let (A in mathtt{A }), (mathtt{A }) is a (sigma )-algebra of sets in (wp ( X);fin )F, F is the class of all finite non-negative measurable functions defined on measurable space (X, ({mathbb { A}})).