 In terms of the Radon–Nikodym derivative,

More generally, the Gaussian measure with mean "μ" ∈ R"n" and variance "σ"2 > 0 is given by

Gaussian measures with mean "μ" = 0 are known as centred Gaussian measures.The Dirac measure "δ""μ" is the weak limit of formula_5 as "σ" → 0, and is considered to be a degenerate Gaussian measure; in contrast, Gaussian measures with finite, non-zero variance are called non-degenerate Gaussian measures.The standard Gaussian measure "γ""n" on R"n"

so Gaussian measure is a Radon measure;


It can be shown that there is no analogue of Lebesgue measure on an infinite-dimensional vector space.