Tame Function (Segal)

A function $f$ on a real Hilbert space $M$ is tame if $f(x)=\bar f(Px)$ for some finite-dimensional subspace $M'$ and projection $P:M\to M'$.

Key properties (paper use):

• Tame functions generate the σ-algebra $\mathfrak R$ of the Gaussian probability space.
• Integrals are defined first on tame functions via finite-dimensional Gaussian integrals.

Example: $f(x)=\exp(i(x,e))$ depends only on the 1D coordinate $(x,e)$.