本书系统阐述了现代高斯测度理论，以完整且详尽的证明呈现了有限维和无限维高斯分布的基本事实。书中涵盖的主题包括线性性质、凸性、线性与非线性变换，以及在高斯过程和扩散过程中的应用。本书适合作为研究生教材或参考著作，包含大量示例、习题和详尽的参考文献，汇集了许多此前未以专著形式呈现的研究成果。This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.