2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77152We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$ with respect to a topology given by certain explicitly written seminorms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on $\bar{K}$. If we deal with Galois extensions then all these objects are Galois-invariant.24 pages, LaTex; to appear in Potential AnalysisFunctional AnalysisNumber TheoryProbabilitytext