A Radon measure \(\mu \) is n-rectifiable if it absolutely continuous with respect to \({\mathcal {H}}^n\) and \)-almost all of \({{\,\mathrm{supp}\,}}\mu can be covered by Lipschitz images \({\mathbb {R}}^n\). In this paper we give two sufficient conditions for rectifiability, both in terms square functions flatness-quantifying coefficients. The first condition involves the so-called \(\alpha ...

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 ...