# Math 607, Real Variables I, Fall 2021.

Taught by Ken Dykema. We meet for lecture TR, 12:45-2:00 in BLOC 110. Office Hours: M 9-10, WF 8-9, or by appointment. Office hourse will be held via Zoom. Registered students will receive the Zoom coordinates by email.

Here is a syllabus.

Here is Folland's list of errata for the textbook.

Assigned homework problems (page numbers refer to the text)

• Homework Set 1, due SEP 8: Problem A (from the first lecture): show every vector space has a basis. From the text: p. 24, # 3, 4, 5. For #3, note that the continuum c is the cardinality of the power set of the natural numbers.

• Homework Set 2, due SEP 15: pp. 27-28, # 7, 9, 10, 14, 15.

• Homework Set 3, due SEP 22: pp. 32-33, # 18, 19, 23, 24.

• Homework Set 4, due SEP 29: pp. 40, # 30, 31, 33.

• Homework Set 5, due OCT 06: pp. 48-49 # 1, 2, 3, 4, 8. To solve for yourself but not to hand in: #6. 7.

• Homework Set 6, due OCT 13: pp. 48-49 # 11; p. 52 # 14.

• Homework Set 7, due OCT 25: p. 52 # 15, 16. pp. 59-60 # 21, 25, 26, 28.

• Homework Set 8, due NOV 01: pp. 63-64, # 32, 33, 34, 37, 38.

• Homework Set 9, due NOV 10: p. 64, # 44. pp. 68-69, # 45, 46. p. 77, # 55, 59. To solve for yourself but not to hand in: p. 69 #49.

• Homework Set 10, due NOV 24: pp. 92-93, # 10, 12, 13, 15, 17. p. 94, # 20.

• Homework Set 11, due DEC 01: p. 100, # 25, and the following extra problem: Suppose mu and nu are positive Borel measures on R^n satisfying mu(E) is less than or equal to nu(E) for all Borel sets E in R^n. Suppose that nu is regular. Show that mu is regular.