Sentence examples for measurable functions and from inspiring English sources

In [3] problem 24.5.6, Ismail proposed the extension of the action of E q y to measurable functions and proving that the only measurable functional solution of the q-analogue of the Cauchy functional equation E q y f ( x ) = f ( x ) f ( y ). is the q-exponential function.

The proposed technique is based on the concept of nonrelatively measurable functions and sequences.

τ as a suitable closure, á la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions, and show that AR is a C*-algebra, and τ extends to a semicontinuous semifinite trace on AR.

holds for all measurable functions and for all functions.

If both functions, and, are nonnegative measurable functions and satisfy and, then (3.1).

Let be the set of all Lebesgue measurable functions and (21).

Let ((Omega, Sigma, mu)) be a measure space, (f:Omegarightarrow[0,1]) be a measurable function, and (p:Omegarightarrowmathbb{R}) be a nonnegative integrable function.

Let ((Omega, Sigma, mu)) be a measure space, (f:Omegarightarrow [0,1]) be a measurable function, and C be a copula.

end{aligned}Here (E_1,ldots,E_m) are spectral measures on Hilbert space, (Psi ) is a measurable function, and (T_1,ldots,T_{m-1}) are bounded linear operators on Hilbert space.

If is a nonnegative measurable function and, then (2.13).

for all and, where is a measurable function and is a strictly monotone mapping.