Mathematics BSc
Course description
2013.

Analysis 4
Hours
lect+pc
Credits
lect+pc
Assessment Specialization Course code
lect/pc
Semester Status
2 + 2 2 + 3 exam +
term grade
applied math. mm1c1an4a
mm1c2an4a
4 compulsory
Strong Weak Prerequisites
Practice class
Strong:
Analysis2L (mm1c1an2) or
Foundations of analysisL (mm1c1ap2)
Lecture
Weak:
practice class
Weak:
Analysis3L-a (mm1c1an3a) or
Analysis3L-p (mm1c1an3m)
Literature
  • A. C. Zaanen: Integration. North Holland Publ. Co., Amsterdam 1967.
Syllabus
  • Surfaces and their area, curves on surfaces.
  • Integration on surfaces. Poincare-Stokes, Gauss-Ostrogradski theorems.
  • Measure theory: measures on sigma-algebras, Lebesgue- and Lebesgue-Stieltjes measure, Borel sets.
  • Integration on measure spaces, Lebesgue integral. Convergence theorems.
  • Lp spaces, their basic properties and completeness.
  • Absolute continuity, Radon-Nikodym theorem.
  • Fubini's theorem.
  • Signed measures, Hahn- and Jordan decomposition.