Does there exist a Borel measure or any valid measure on an infinite dimensional Banach space such that a bounded open set in this space has a positive measure ?



Measures on infinite dimensional Banach spaces
The negative result mentioned in the comment by Zen Harper, is about invariant measures, non-existent on infinite-dimensional Banach spaces. If one does not require the invariance, there is no problem. See, for example, the calculation of the Gaussian measure of a ball in the paper


<http://titan.math.udel.edu/~wli/papers/94-shifted-Kuelbs-Li-Linde.pdf>


