Measure theory in topological vector spaces

In mathematics, measure theory in topological vector spaces refers to the extension of measure theory to topological vector spaces. Such spaces are often infinite-dimensional, but many results of classical measure theory are formulated for finite-dimensional spaces and cannot be directly transferred. This is already evident in the case of the Lebesgue measure, which does not exist in general infinite-dimensional spaces.

The article considers only topological vector spaces, which also possess the Hausdorff property. Vector spaces without topology are mathematically not that interesting because concepts such as convergence and continuity are not defined there.