Notes on functional integration

This work is devoted to the construction of an “integral” on an infinite-dimensional space which combines the approaches proposed earlier and at the same time is the simpliest one. We give a new definition of the construction and study its properties on a special class of functionals. We also consider the introduction of a quasi-scalar product, an orthonormal system, and applications in physics (path integral, loop space, functional derivative). In addition the paper contains a discussion of generalized functionals.