Abstract
This chapter discusses the integral of an operational function and its applications. It is more convenient to introduce the notion of integral in the operational calculus by a suitable generalization of the Lebesgue integral. It is possible, however, to avoid the theory of the Lebesgue integral if one is restricted to a certain particular class of operational functions. One shall define a certain class of functions f(λ, t) that will be denoted by (H). A function f(λ, t) will be said to be a function of class (H) in the domain D α ≤ λ ≤ β, 0 ≤ t < ∞. It is found that if 1° every partial domain D0, α ≤ λ ≤ β, 0 ≤ t < t0 can be intersected by at most a finite number of straight lines parallel to the axes λ and t and containing infinitely many points of discontinuity of the function f(λ, t).
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