Sentence examples for be a nonnegative integrable from inspiring English sources

Let be a nonnegative integrable function with.

Let be a nonnegative integrable function on with.

Let and let be a nonnegative integrable function on such that satisfies the -condition for some.

To define the -condition on, we let be a nonnegative integrable function on.

Let be a positive increasing concave nonlinear function on, and let be a nonnegative integrable function on with.

Let (f,g:[a,b]rightarrow[0,1]) be two synchronous functions, and (p:[a,b]rightarrowmathbb{R}) be a nonnegative integrable function.

When ω is a nonnegative, integrable function on ([0, 1]) and not identically zero, we say that ω is a weight.

The most fundamental averaging operator is Hardy operator defined by mathcal{H}f(x):= frac{1}{x} int_{0}^{x}f(t),dt, where the function f is a nonnegative integrable function on (mathbb{R}^) and (x>0).

The most fundamental averaging operator is the Hardy operator defined by H ( f ) ( x ) = 1 x ∫ 0 x f ( t ) d t, where the function f is a nonnegative integrable on R + = ( 0, ∞ ) and x > 0. A classical inequality, due to Hardy [1], states that ∥ H ( f ) ∥ L p ≤ p p − 1 ∥ f ∥ L p. holds for 1 < p < ∞, and the constant p p − 1 is best possible.

Let f be a nonnegative locally integrable function.

Let (upsilon:Jrightarrow[0,infty)) be a real function and (omega(cdot,cdot)) be a nonnegative, locally integrable function on J.