國立高雄大學圖資館 |

Language: English

Back

Measure, integration and a primer on...

Gentili, Stefano.

Measure, integration and a primer on probability theory.Volume 1

Record Type:	Electronic resources : Monograph/item
Title/Author:	Measure, integration and a primer on probability theory.by Stefano Gentili.
Author:	Gentili, Stefano.
Published:	Cham :Springer International Publishing :2020.
Description:	xi, 463 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functional analysis.
Online resource:	https://doi.org/10.1007/978-3-030-54940-4
ISBN:	9783030549404$q(electronic bk.)

Measure, integration and a primer on probability theory.Volume 1
Gentili, Stefano.

Measure, integration and a primer on probability theory.Volume 1[electronic resource] /by Stefano Gentili. - Cham :Springer International Publishing :2020. - xi, 463 p. :ill., digital ;24 cm. - UNITEXT - La Matematica per il 3+2 ;v.125. - UNITEXT - La Matematica per il 3+2 ;v.125..

Part I Sets: 1 Round-up of topology -- 2 Types of sets -- Part II Borel sets and Baire functions on R: 3 Borel sets in R -- 4.Baire functions on R -- 5 Borel functions and Baire functions -- Part III Families of sets: 6 Semi-algebras and algebras of sets -- 7. Monotone classes and o-algebras -- Part IV Measure theory: 8. Set functions and measure -- 9 The Lebesgue measure -- 10. Measurable functions -- Part V Theory of integration: 11 The Lebesgue integral -- 12 Comparing notions of integral -- Part VI Fundamental theorems of integral calculus: 13 Bounded variations and absolute continuity -- 14 Fundamental theorems of calculus for the Lebesgue integral -- Part VII Appendices: A Compact and totally bounded metric spaces -- B Urysohn's lemma and Tietze's theorem.

The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject from a wider angle, thus appreciating the human side of major figures in Mathematics. The style in which topics are addressed, albeit informal, always maintains a rigorous character. The attention placed in the careful layout of the logical steps of proofs, the abundant examples and the supplementary remarks disseminated throughout all contribute to render the reading pleasant and facilitate the learning process. The exposition is particularly suitable for students of Mathematics, Physics, Engineering and Statistics, besides providing the foundation essential for the study of Probability Theory and many branches of Applied Mathematics, including the Analysis of Financial Markets and other areas of Financial Engineering.

ISBN: 9783030549404$q(electronic bk.)

Standard No.: 10.1007/978-3-030-54940-4doiSubjects--Topical Terms:

200585
Functional analysis.

LC Class. No.: QA326 / .G46 2020

Dewey Class. No.: 512.55

Measure, integration and a primer on probability theory.Volume 1
LDR:02800nmm a2200337 a 4500 001 589665
003 DE-He213
005 20210311134010.0
006 m d
007 cr nn 008maaau
008 210601s2020 sz s 0 eng d
020 $a 9783030549404$q(electronic bk.)
020 $a 9783030549398$q(paper)
024 7 $a 10.1007/978-3-030-54940-4 $2 doi
035 $a 978-3-030-54940-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA326 $b .G46 2020
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 512.55 $2 23
090 $a QA326 $b .G338 2020
100 1 $a Gentili, Stefano. $3 881637
245 1 0 $a Measure, integration and a primer on probability theory. $n Volume 1 $h [electronic resource] / $c by Stefano Gentili.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xi, 463 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT - La Matematica per il 3+2 ; $v v.125
505 0 $a Part I Sets: 1 Round-up of topology -- 2 Types of sets -- Part II Borel sets and Baire functions on R: 3 Borel sets in R -- 4.Baire functions on R -- 5 Borel functions and Baire functions -- Part III Families of sets: 6 Semi-algebras and algebras of sets -- 7. Monotone classes and o-algebras -- Part IV Measure theory: 8. Set functions and measure -- 9 The Lebesgue measure -- 10. Measurable functions -- Part V Theory of integration: 11 The Lebesgue integral -- 12 Comparing notions of integral -- Part VI Fundamental theorems of integral calculus: 13 Bounded variations and absolute continuity -- 14 Fundamental theorems of calculus for the Lebesgue integral -- Part VII Appendices: A Compact and totally bounded metric spaces -- B Urysohn's lemma and Tietze's theorem.
520 $a The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject from a wider angle, thus appreciating the human side of major figures in Mathematics. The style in which topics are addressed, albeit informal, always maintains a rigorous character. The attention placed in the careful layout of the logical steps of proofs, the abundant examples and the supplementary remarks disseminated throughout all contribute to render the reading pleasant and facilitate the learning process. The exposition is particularly suitable for students of Mathematics, Physics, Engineering and Statistics, besides providing the foundation essential for the study of Probability Theory and many branches of Applied Mathematics, including the Analysis of Financial Markets and other areas of Financial Engineering.
650 0 $a Functional analysis. $3 200585
650 0 $a Probabilities. $3 182046
650 0 $a Measure theory. $3 182047
650 0 $a Fourier analysis. $3 184626
650 1 4 $a Measure and Integration. $3 273777
650 2 4 $a Fourier Analysis. $3 273776
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a UNITEXT - La Matematica per il 3+2 ; $v v.125. $3 881638
856 4 0 $u https://doi.org/10.1007/978-3-030-54940-4
950 $a Mathematics and Statistics (SpringerNature-11649)