Title Statements
- Full title :Measure spaces and measurable functions / Robert R. Reitano.
Edition Statements
- Publication Date:2022.
Publication Statements
- Publisher(s):Chapman & Hall/CRC
- Place of Publication:Boca Raton
- Language:eng
- Publication Date:2022.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9781000596861, 1000596869, 1000596915, 9781000596915, 1003257747, 9781003257745
- DOI:10.1201/9781003257745
- oclc:on1352041705
- Dewey Decimal:322.015195
Table of Contents
<P>Preface <BR>Introduction </P><P>1 The Notion of Measure 0 <BR>1.1 The Riemann Integral <BR>1.2 The Lebesgue Integral </P><P>2 Lebesgue Measure on R 13<BR>2.1 Sigma Algebras and Borel Sets <BR>2.2 Definition of a Lebesgue Measure <BR>2.3 There is No Lebesgue Measure on -(P(R)<BR>2.4 Lebesgue Measurable Sets: ML(R) $ -(P(R)) <BR>2.5 Calculating Lebesgue Measures <BR>2.6 Approximating Lebesgue Measurable Sets <BR>2.7 Properties of Lebesgue Measure <BR>2.7.1 Regularity <BR>2.7.2 Continuity <BR>2.8 Discussion on B(R) &ML(R) </P><P>3 Measurable Functions 55<BR>3.1 Extended Real-Valued Functions <BR>3.2 Equivalent Definitions of Measurability <BR>3.3 Examples of Measurable Functions <BR>3.4 Properties of Measurable Functions <BR>3.4.1 Elementary Function Combinations <BR>3.4.2 Function Sequences <BR>Function Sequence Behaviors <BR>Function Sequence Measurability Properties <BR>3.5 Approximating Lebesgue Measurable Functions <BR>3.6 Distribution Functions of Measurable Functions </P><P>4 Littlewood.s Three Principles <BR>4.1 Measurable Sets <BR>4.2 Convergent Sequences of Measurable Functions <BR>4.3 Measurable Functions </P><P>5 Borel Measures on R <BR>5.1 Functions Induced by Borel M…
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