A weak form of this property is present for a function if that function is bounded and its set of discontinuity points is a zero set, and that version of this property is absent for the characteristic function of the rationals.
According to Holder's inequality, the product of two functions from the Banach-normed spaces L-sub-p and L-sub-q has this property if p and q are conjugate indices. A weak form of this property is present for a function if that function is bounded and its set of discontinuity points is a zero set, and that version of this property is absent for the characteristic function of the rationals. If a sequence of functions converges everywhere to a real-valued measurable function f and each function in the sequence is absolutely bounded by a function with this property, then f has this property as well, according to Lebesgue's Dominated Convergence theorem. A function can also be said to have the proper form of this property with respect to the Jordan measure if the limit of its Riemann sum is finite. For ten points, identify this property possessed by those functions whose anti-derivative can be computed.
According to Holder's inequality, the product of two functions from the Banach-normed spaces L-sub-p and L-sub-q has this property if p and q are conjugate indices.
integrable [or integrability]