Let p ∈ L ( [ a, b ] ; R + ), τ : [ a, b ] → [ a, b ] be a measurable function, and let the functional h be defined by formula (4), where λ > 0 and h 0, h 1 ∈ P F a b are such that the inequalities h ( 1 ) > 1, 0 < h 0 ( 1 ) < 1. are fulfilled.
Let g ∈ L ( [ a, b ] ; R + ), μ : [ a, b ] → [ a, b ] be a measurable function, and let the functional h be defined by formula (4), where λ > 0 and h 0, h 1 ∈ P F a b are such that inequalities (11) are fulfilled.
Let p ∈ L ( [ a, b ] ; R + ), τ : [ a, b ] → [ a, b ] be a measurable function, and let the functional h be defined by formula (4), where λ > 0 and h 0, h 1 ∈ P F a b are such that inequalities (11) are fulfilled.
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.
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).
with and measurable functions and This equation is a particular case of (2.14).
