Measure spaces and measurable functions. (2022)

• Record Type: Book
• Further Information: Note: Robert R. Reitano.
• Authors: Reitano, Robert R, 1950-
• Contents: Preface; Introduction 1 The Notion of Measure 0; 1.1 The Riemann Integral; 1.2 The Lebesgue Integral 2 Lebesgue Measure on R 13; 2.1 Sigma Algebras and Borel Sets; 2.2 Definition of a Lebesgue Measure; 2.3 There is No Lebesgue Measure on _(P(R); 2.4 Lebesgue Measurable Sets: ML(R) $ _(P(R)); 2.5 Calculating Lebesgue Measures; 2.6 Approximating Lebesgue Measurable Sets; 2.7 Properties of Lebesgue Measure; 2.7.1 Regularity; 2.7.2 Continuity; 2.8 Discussion on B(R) &ML(R) 3 Measurable Functions 55; 3.1 Extended Real-Valued Functions; 3.2 Equivalent Definitions of Measurability; 3.3 Examples of Measurable Functions; 3.4 Properties of Measurable Functions; 3.4.1 Elementary Function Combinations; 3.4.2 Function Sequences; Function Sequence Behaviors; Function Sequence Measurability Properties 3.5 Approximating Lebesgue Measurable Functions; 3.6 Distribution Functions of Measurable Functions 4 Littlewood.s Three Principles; 4.1 Measurable Sets; 4.2 Convergent Sequences of Measurable Functions; 4.3 Measurable Functions 5 Borel Measures on R; 5.1 Functions Induced by Borel Measures; 5.2 Borel Measures from Distribution Functions; 5.3 Consistency of Borel Measure Constructions; 5.4 Approximating Borel Measurable Sets; 5.5 Properties of Borel Measures; 5.6 Differentiable F-Length and Lebesgue Measure 6 Generating Measures by Extension; 6.1 Recap of Lebesgue and Borel Constructions; 6.2 Extension Theorems; 6.3 Summary - Construction of Measure Spaces; 6.4 Approaches to Countable Additivity; 6.5 Completion of a Measure Space 7 Finite Products of Measure Spaces; 7.1 Product Space Semi-Algebras; 7.2 Properties of the Semi-Algebra; 7.3 Measure on the Algebra A; 7.4 Extension to a Measure on the Product Space; 7.5 Well-Definedness of _-Finite Product Measure Spaces; 7.6 Products of Lebesgue and Borel Measure Spaces; 8 Borel Measures on Rn; 8.1 Rectangle Collections that Generate B(Rn); 8.2 Borel Measures and Induced Functions; 8.3 Properties of General Borel Measures on Rn 9 Infinite Products of Probability Spaces; 9.1 A Naive Attempt at a First Step; 9.2 A Semi-Algebra A0; 9.3 Finite Additivity of _A on A for Probability Spaces; 9.4 Free Countable Additivity on Finite Probability Spaces; 9.5 Countable Additivity on A+ in Probability Spaces on R 9.6 Extension to a Probability Measure on RN; 9.7 Probability of General Rectangles References;
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2022
• Extent: 1 online resource
• Subjects: 322.015195; Finance -- Mathematical models; Measure theory; Algebraic spaces
• Languages: English
• ISBNs: 9781000596915; 9781000596861; 9781003257745
• Related ISBNs: 9781032191201
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.