The Resource Real Analysis, by Peter A Loeb, (electronic resource)

# Real Analysis, by Peter A Loeb, (electronic resource) Resource Information The item Real Analysis, by Peter A Loeb, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.

Label
Real Analysis
Title
Real Analysis
Statement of responsibility
by Peter A Loeb
Creator
Subject
Language
eng
Summary
This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.--
Member of
Assigning source
Provided by publisher
Loeb, Peter A
Image bit depth
0
Literary form
non fiction
• Mathematics
• Functional analysis
• Measure theory
• Functions of real variables
Label
Real Analysis, by Peter A Loeb, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent.
Contents
Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References
Control code
978-3-319-30744-2
Dimensions
unknown
Extent
1 online resource (xii, 274 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319307442
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
• c
Other control number
10.1007/978-3-319-30744-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)949407231
Label
Real Analysis, by Peter A Loeb, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent.
Contents
Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References
Control code
978-3-319-30744-2
Dimensions
unknown
Extent
1 online resource (xii, 274 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319307442
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
• c
Other control number
10.1007/978-3-319-30744-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)949407231