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Provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures.

Measure theory is a classical area of mathematics that continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives a systematic presentation of modern measure theory  as it has developed over the past century and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the bas...

Provides a systematic exposition of the modern theory of Gaussian measures. It presents 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.

Provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure, in the infinite dimensional case new phenomena arise. It also provides for the first time a detailed account of the theory of differentiable measures, initiated by S. V. Fomin in ...

Gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter.

Measure theory is a classical area of mathematics that continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives a systematic presentation of modern measure theory  as it has developed over the past century and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the bas...