Table of contents

The course is connected to the following study programs

  • Industrial Mathematics, Bachelor's Programme

Teaching language

Norwegian or English

Recommended previous knowledge

60 sp in mathematics including Real Analysis.

Learning outcomes

Upon successful completion of the course, the student will be able to

  • Explain and apply the Lebesgue integral for positive measures, included product measures.
  • Explain the convergence theorems (the monotone case, Fatou’s lemma and Lebesgue' dominated convergence) as well as the Fubini-Tonelli theorem.
  • Apply measure- and integration theory at fundamental parts of probability theory.
  • Know the measure theoretic definitions of probability, independence, random variable, as well as various ways of describing the probability distribution of random variables.
  • apply methods in order to treat and describe limits of sequences of random variables, in particular the law of large numbers, the central limit theorem.

Contents

Lebesgue integral when measure and sigma-algebra are given, convergence theorems, product measure and integration on product spaces. Probability described by measure theoretic concepts, with themes like distribution and density, convergence of sequences of random variables, laws of great numbers, the central limit theorem.

Teaching and learning methods

Lectures, group work, project with applications to industrial mathematics and compulsory submissions. Estimated workload of the course is 267 hours.

Examination requirements

Mandatory hand-ins must be approved. See Canvas for details.

Examinations

Individual, oral exam. Graded assessment.

Student evaluation

The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.

Offered as a free-standing course

Yes. Subject to availability or capacity.
Last updated from FS (Felles studentsystem) Oct. 15, 2026 2:31:23 PM