Advances in Analysis, Probability and Mathematical Physics: Contributions of Nonstandard Analysis (Hardcover, 1995)

Preface. Part I: Analysis. Singular traces and nonstandard analysis; S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti. Navier--Stokes equations; M. Capinski, N. Cutland. Hyperfinite approximations of commutative topological groups; E.I. Gordon. A note on the myope topology; T. Norberg. Nonlinear theories of generalized functions; M. Oberguggenberger. A nonstandard approach to the Pettis integral; H. Osswald. A counterexample to the spectral mapping theorem revisited from a nonstandard point of view; H. Ploss. Nonstandard polynomials in several variables; H. Render. An existence result for a class of partial differential equations with smooth coefficients; T. Todorov. On the generation of topology by external equivalence relations; B. Wietschorke. Nonstandard hulls of Lebesgue--Bochner spaces; B. Zimmer. Part II: Probability Theory. A nonstandard approach to diffusions on manifolds and nonstandard heat kernels; H. Akiyama. A nonstandard approach to the Malliavin Calculus; N.J. Cutland, Siu-Ah Ng. Ergodic transformations in AST; M. Kalina. Nonstandard characterization for a general invariance principle; D. Landers, L. Rogge. Andersons's Brownian motion and the infinite dimensional Ornstein--Uhlenbeck process; T. Lindstrøm. Two applications of NSA in the theory of stochastic dynamical systems; A. Ponosov. Nonstandard methods and the space of experiments; D.A. Ross. Part III: Mathematical Physics. Infinite range forces and strong L1-asymptotics for the space--homogeneous Boltzmann equation; L. Arkeryd. A nonstandard analysis approach to the theory of quantum meanfield systems; M.P.H. Wolff. Subject Index.