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Advanced Real Analysis II

This course continues on from Advanced Real Analysis I, considering both measure theory and functional analysis more in depth, and with several advanced applications.

The course covers signed measure, Hahn decomposition, measures on metric spaces, Radon-Nikodym theorem, Lebesgue decomposition, dual spaces, weak topologies, Banach-Alaoglu theorem, adjoint operators, compact operators and their spectrum, Fredholm alternative, Hilbert spaces and operators on Hilbert spaces, spectral theory of self-adjoint operators in Hilbert space, Fredholm determinant, unlimited operators.

This course is given jointly by Stockholm University and KTH, and part of the course is given at KTH. The exam, however, is given at SU. More information can be found on the course web before the start of the semester, see link below.

  • Course structure

    The course consists of one element.

    Teaching format

    Instruction is given in the form of lectures and exercises.


    The course is assessed through written assignments and as written and oral exams.


    A list of examiners can be found on

    Exam information

  • Schedule

    The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.

    Schedule for the part of the course that is given at Stockholm University can be found below. The part given at KTH may have a separate schedule, see the course web.

  • Course literature

    Note that the course literature can be changed up to two months before the start of the course.

    Course literature Department of Mathematics

  • More information

    New student
    During your studies

    Course web

    We do not use Athena, you can find our course webpages on

    There may be another course web for the part of the course given at KTH. If so, this should be linked from the course web at Stockholm University found via the link above.

  • Contact