qThis book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's qstochastic calculus of variationsq developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.q--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights ReservedAs examples, we can take n(dx) = e*rdx, e~*s~dx, dx, and e~^dx. (b) By hypothesis, /xi(dx) = e~axfi(dx) and u\(dx) a e~axu(dx) are bounded measures. Their images ^(dx) and U2(dx) under the mapping x ia Ar e~x are concentrated in [0, 1] .

Title | : | Exercises and Solutions Manual for Integration and Probability |

Author | : | Gerard Letac, Paul Malliavin |

Publisher | : | Springer Science & Business Media - 1995-06-01 |

Continue