Suppose that we seek a translation-invariant, strictly positive, locally finite measure on the real line.

Since δ is probability measure, it is also a locally finite measure.

In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure.

An abstract Wiener space is a mathematical object in measure theory, used to construct a "decent", strictly positive and locally finite measure on an infinite-dimensional vector space.

Since a probability measure is globally finite, and hence a locally finite measure, every probability measure on a Radon space is also a Radon measure.