strictly positive measure

Intuitively, a strictly positive measure is one that is "nowhere zero", or that it is zero "only on points".

Then a measure μ on (X, Σ) is called strictly positive if every non-empty open subset of X has strictly positive measure.

Wiener measure on the space of continuous paths in R is a strictly positive measure - Wiener measure is an example of a Gaussian measure on an infinite-dimensional space.