Explore: Bochner Integrals

the limit of integrals of simple functions. The Bochner integral provides the mathematical foundation for extensions of basic integral transforms into

Chelsea Pub. Co. Bochner, S. (1959). Lectures on Fourier integrals; with an author's supplement on monotonic functions, Stieltjes integrals, and harmonic

The integral is also called the weak integral in contrast to the Bochner integral, which is the strong integral. Let f : X → V {\displaystyle f:X\to V}

The most commonly used definitions are Riemann integrals and Lebesgue integrals. The Riemann integral is defined in terms of Riemann sums of functions

Common integrals in quantum field theory are all variations and generalizations of Gaussian integrals to the complex plane and to multiple dimensions.

integral without mentioning null sets. He also proved the change of variables theorem for multiple Bochner integrals and Fubini's theorem for Bochner

The Bochner–Riesz mean is a summability method often used in harmonic analysis when considering convergence of Fourier series and Fourier integrals. It

In mathematics, the Bochner–Martinelli formula is a generalization of the Cauchy integral formula to functions of several complex variables, introduced

In mathematics, Bochner spaces are a generalization of the concept of L p {\displaystyle L^{p}} spaces to functions whose values lie in a Banach space

selection of }}\varphi \right\}} where the integrals ∫ X f d μ {\displaystyle \int _{X}fd\mu } are Bochner integrals. Example: let the underlying measure space