Math 5320, Basic Real Analysis 2

Semester 2, 2005-06

Course Lecturer:

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227
Email: packer@euclid.colorado.edu
URL: http://spot.colorado.edu/~packer

Course Information:
 This course is meant to continue the study of analysis of real-valued functions of one or several variables, with an emphasis on Lebesgue measure and Lebesgue integration on the real line and R^n. Topics to be covered include:
L^p - spaces, definitions and examples; Minkowski's inequality, Holder's inequality; Arzela-Ascoli Theorem, Stone-Weierstrass Theorem, Signed measures, definitions and basic properties, Hahn decomposition Theorem, Jordan decompostion, mutually singular measures, Jordan decomposition Theorem, comparison of measures, absolutely continuous measures, Radon-Nikodym Theorem, Lebesgue decomposition theorem; product measures: Fubini's Theorem, Tonelli's Theorem, applications of Fubini Theorem to integral operators.

Prerequisite:
 Math 6310, or instructor consent.

Course Text:
 We will use as a primary text the book "Real Analysis", by H.L. Royden, Third Edition, covering most of Chapters 6, parts of Chapters 7 and 9, and most of Chapters 11, and 12.

Assessment: Lecture Hours and Venue:
MWF 10 a.m.-11 a.m. ECCR 137

Office Hours:
Mon, Wed., Fri. 11 a.m. -12 noon, and by appointment.

Homework:
Some Important Names associated with Real Analysis :

Various other matters :
For informations on students with disabilities, religious obligations, honor code, student classroom and course-related behavior, and discrimination and harassment issues, see the university pages on these matters at:
Students With Disabilities
www.Colorado.EDU/disabilityservices.

Missed Exams:
If you know that you are going to miss an exam or cannot take the final exam at the scheduled time, please notify me at least two weeks in advance. If you miss a midterm exam for any acceptable reason (e.g. religious obligation, documented illness), you will be given an average score based on your performance in the other midterm. If you miss all midterm exams for acceptable reasons, your course grade will be based entirely on your final exam score. If you miss the final exam and have not rescheduled it in advance, you will score zero on the final.

Religious Obligations:

Campus policy regarding religious observances requires that faculty make every effort to reasonably and fairly deal with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance. In this class, you should notify me of any conflict at least two weeks in advance. See full details at http://www.colorado.edu/policies/fac_relig.html.

Student Classroom and Course-Related Behavior:
Students and faculty each have responsibility for maintaining an appropriate learning environment. Students who fail to adhere to such behavioral standards may be subject to discipline. Faculty have the professional responsibility to treat all students with understanding, dignity and respect, to guide classroom discussion and to set reasonable limits on the manner in which they and their students express opinions. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name. Your instructor will gladly honor your request to address you by an alternate name or gender pronoun. Please advise your instructor of this preference early in the semester so that appropriate changes may be made to the records. See polices at http://www.colorado.edu/policies/classbehavior.html and at http://www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code

Honor Code:
All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior. All incidents of academic misconduct shall be reported to the Honor Code Council (honor@colorado.edu; 303-725-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at http://www.colorado.edu/policies/honor.html and at http://www.colorado.edu/academics/honorcode/

Statement on Discrimination and Harassment:
The University of Colorado at Boulder policy on Discrimination and Harassment (http://www.colorado.edu/policies/discrimination.html), the University of Colorado policy on Sexual Harassment and the University of Colorado policy on Amorous Relationships applies to all students, staff and faculty. Any student, staff or faculty member who believes s/he has been the subject of discrimination or harassment based upon race, color, national origin, sex, age, disability, religion, sexual orientation, or veteran status should contact the Office of Discrimination and Harassment (ODH) at 303-492-2127 or the Office of Judicial Affairs at 303-492-5550. Information about the ODH and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh.

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Last modified January 17, 2006.