Gaussian Measures in Finite and Infinite Dimensions

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Focusing on Gaussian measures, this text serves as an introduction for students in a one-semester course. It highlights the role of Fourier analysis in probabilistic results and explores Gaussian measures in both finite and infinite dimensional spaces. Key properties that are dimension independent are emphasized, and Gaussian processes are constructed. The book also delves into Gaussian measures on Banach spaces, adopting insights from I. Segal and L. Gross. It is designed for those with a background in Lebesgue integration and functional analysis, offering techniques applicable beyond Gaussian measures.