This is a QR code. A QR Code is a 2-dimensional barcode, which has encoded in it a URL (web address), text, or other information. It can be read by a QR code scanner, including QR scanner smartphone apps. Once you have an app installed on your smartphone, open the app and hold your phones camera over a QR code to read it. Most QR codes youll come across have a URL encoded, so chances are when you read the QR code it will take you to a web page.
Reviewed by members of Editorial board for inclusion in MERLOT.
Useful material in MERLOT
Click to get more information on the MERLOT Editors' Choice Award in a new window.
Click to get more information on the MERLOT Classics Award in a new window.
Click to get more information on the MERLOT JOLT Award in a new window.
Search all MERLOT
Click here to go to your profile
Click to expand login or register menu
Select to go to your workspace
Click here to go to your Dashboard Report
Click here to go to your Content Builder
Click here to log out
Please give at least one keyword of at least three characters for the search to work with. The more keywords you give, the better the search will work for you.
select OK to launch help window
You are now going to MERLOT Help. It will open in a new window
For optimal performance of MERLOT functionality, use IE 9 or higher, or Safari on mobile devices
This is a free, online textbook that is part of a series. According to the author, it "completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach...
This is a free, online textbook that is part of a series. According to the author, it "completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and integration in the following chapter follows an innovative approach, carefully choosing one of the equivalent definitions of measurable functions that allows the most intuitive development of the material. Fubini's theorem, the Radon-Nikodym theorem, and the basic convergence theorems (Fatou's lemma, the monotone convergence theorem, dominated convergence theorem) are covered. Finally, a chapter relates antidifferentiation to Lebesgue theory, Cauchy integrals, and convergence of parametrized integrals. Nearly 500 exercises allow students to develop their skills in the area.
College Lower Division,
College Upper Division
Not specified at this time
Technical Requirements: According to the author,"All uses of this text are subject to the Terms and Conditions contained in this text. As part of these terms, we offer this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university."