Sentence examples for Lebesgue measurable function from inspiring English sources

We assume that each (mu _j) is (sigma )-finite; hence, by Radon Nikodym's Theorem, we have the decomposition (dmu _j= d(mu _j)_s + w_j ds), where ((mu _j)_s) is singular with respect to Lebesgue measure and (w_j) is a non-negative Lebesgue measurable function.

Let be a non (Lebesgue) measurable function.

Let p : → [ 1, + ∞ ) be a Lebesgue measurable function.

If and, we define as being the subspace of of the Lebesgue measurable function, satisfying (2.1).

Throughout this paper, (L^{2}[0,r_{0};r^{2}]) denotes the Hilbert space of Lebesgue measurable function φ with weight (r^{2}) on ([0,r_{0}]).

Theorem 2 Let 〈 H ; 〈 ⋅, ⋅ 〉 〉 be a real or complex Hilbert space, Ω ⊂ R n a Lebesgue measurable set and ρ : Ω → [ 0, ∞ ) a Lebesgue measurable function with ∫ Ω ρ ( s ) d s = 1.

Let be the set of all Lebesgue measurable functions.

Let be all Lebesgue measurable functions from to.

Let be the linear space of all Lebesgue measurable functions, identifying the functions equal almost everywhere.

Let denote the space of all real Lebesgue measurable functions defined on to.

Let P be the set of all Lebesgue measurable functions p : Ω → [1, +∞].