Abstract. Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in t...

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the˜∂-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for f...

The integral representation of Choquet operators defined on a space C(X) is established by using the Choquet-Bochner real-valued function with respect to vector capacity.

Abstract. It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a preassigned ε of the integral, with the sum for the local errors also less than ε. All of this follows from the ubiquity of Lebesgue points, which is a co...

Riemann, Lebesgue, Denjoy, Henstock–Kurzweil, McShane, Feynman, Bochner. There are well over 100 named integrals. Why so many? Some are of historical interest and have been superseded by better, newer ones. The Harnack integral is subsumed by the Denjoy. Some are equivalent, as are McShane and Lebesgue in Rn, and Denjoy, Perron, Henstock–Kurzweil in R. Some are designed to work in special space...

Abstract A “Bochner-type” integral for vector lattice-valued functions with respect to (possibly infinite) measures is presented abstract convergences, satisfying suitable axioms, and some fundamental properties are studied. Moreover, by means of this integral, convergence results on operators in modulars proved. Some applications given moment kernels the Brownian motion.

The purpose of this paper is to establish an existence result for nonconvex variational problems with Bochner integral constraints in separable Asplund spaces via the Euler–Lagrange inclusion, under the saturation hypothesis on measure spaces, which makes the Lyapunov convexity theorem valid in Banach spaces. The approach is based on the indirect method of the calculus of variations.

The representation of linear operators, on the Banach space of Bochner integrable functions, has been the object of much study for the past fifty years. Dunford and Pettis began this investigation in 1940 with the representation of weakly compact and norm compact operators on L1(R) by a Bochner integral, see [6,8]. Andrews has extended their study to the case of the space L1(E), of E-valued, Bo...