Sentence examples similar to measurable function defined over from inspiring English sources

Let J : = [ 0, 1 ] and L 1 ( J, E ) denote the Banach space of real-valued Lebesgue integrable functions on the interval J, L ∞ ( J, E ) denote the Banach space of real-valued essentially bounded and measurable functions defined over J with the norm ∥ ⋅ ∥ L ∞.

where the kernel is a nonnegative measurable function defined for and the summation is over all ordered -tuples.

where the kernel K ( x, y ) is a nonnegative measurable function defined for x ≠ y, and the summation is over all ordered l-tuples I.

where the kernel K ( x, y ) is a nonnegative measurable function defined for x ≠ y, ħ J ( x ) is defined on Θ ⊂ R n and the summation is over all ordered ℓ-tuples J.

where the kernel K ( x, y ) is a non-negative measurable function defined for x ≠ y, ħ J ( x ) is defined on Θ ⊂ R n and the summation is over all ordered ℓ-tuples J.

Let ν(x) is a measurable function defined on a subset Θ ⊂ ℝ n.

Suppose that Ω x) is a real valued and measurable function defined on ℝ n.

Suppose f is a measurable function defined on (mathbb{R}^{n}_{k,+}).

Let be a positive constant, and let be a measurable function defined on.

Let λ i,z (t) be a bounded measurable function defined on Open image in new window, which takes values on (−1,∞), where i∈{1,I}.

where a ( x ) are bounded measurable functions defined in G.