Riemann integration, Lebesgue integration
line integral/contour integration
integration of differential forms
integration over supermanifolds, Berezin integral, fermionic path integral
Kontsevich integral, Selberg integral, elliptic Selberg integral
integration in ordinary differential cohomology
integration in differential K-theory
The Wiener measure is a measure on the space of continuous paths in a given manifold. The Lebesgue integral with respect to Wienerâ€™s measure is called the Wiener integral.
The Wiener measure serves to make precise the path integral quantization for the (charged) non-relativistic particle (that of the relativistic particle may be amenable to Wiener measure methods via Wick rotation, i.e. analytic continuation to imaginary time. ).
PlanetMath Wiener measure
A textbook account in the context of path integral quantization is