Super-Gaussian decay of exponentials: A sufficient condition

In this article, we present a sufficient condition for the exponential exp⁡(−f) to have tail decay stronger than any Gaussian, where f is defined on locally convex space X and grows faster squared seminorm X. particular, our result proves that exp⁡(−p(x)2+ε+αq(x)2) integrable all α,ε>0 w.r.t. Radon Gaussian measure nuclear X, if p q are continuous seminorms with compatible kernels. This can be viewed as an adaptation of Fernique's theorem and, example, has applications in quantum field theory.