Studying online

There are now 2 possible online modes for units:

Units with modes Online timetabled and Online flexible are available for any student to self-enrol and study online.

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Unit Overview


This unit provides students with foundations in metric spaces and measure theory. Topics include norms and metrics, metric spaces, completeness, compactness, the contraction mapping principle and its consequences, Lebesgue measure, measurable sets, sigma-algebras, repeated integration, product measure, Fatou's Lemma, Dominated Convergence Theorem, Monotone Convergence Theorem, Lebesgue points, differentiation Theorem, convolution and approximation of the identity.

6 points
Not available in 2024UWA (Perth)Face to face
Details for undergraduate courses
  • Level 2 core unit in the Mathematics major sequence
  • Level 2 option in the Mathematics major sequence

Students are able to (1) explain and exploit the notions of measure; (2) provide examples of measurable and non measurable sets; (3) utilize the notion of product measure and the theorems of Fubini and Tonelli; (4) exploit Fatou's Lemma, Dominated Convergence Theorem and Monotone Convergence Theorem to compute limits of sequence of functions; and (5) exploit the notion of Lebesgue points and the differentiation theorem to detect the density of a measure.


Indicative assessments in this unit are as follows: (1) tests and (2) final exam. Further information is available in the unit outline.

Student may be offered supplementary assessment in this unit if they meet the eligibility criteria.

Unit Coordinator(s)
Professor Luchezar Stoyanov
Unit rules
MATH1011 Multivariable Calculus
or MATX1011 Multivariable Calculus
or MATH1013 Mathematical Analysis
MATH1012 Mathematical Theory and Methods
or MATX1012 Mathematical Theory and Methods
or MATH1014 Algebra
MATH2031 Introduction to Pure Mathematics
Contact hours
lectures: 3 hours per week
workshops: 2 hours per week
  • The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
  • All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
  • Unit readings, including any essential textbooks, are listed in the unit outline for each unit, one week prior the commencement of study. The unit outline will be available via the LMS and the UWA Handbook one week prior the commencement of study. Reading lists and essential textbooks are subject to change each semester. Information on essential textbooks will also be made available on the Essential Textbooks. This website is updated regularly in the lead up to semester so content may change. It is recommended that students purchase essential textbooks for convenience due to the frequency with which they will be required during the unit. A limited number of textbooks will be made available from the Library in print and will also be made available online wherever possible. Essential textbooks can be purchased from the commercial vendors to secure the best deal. The Student Guild can provide assistance on where to purchase books if required. Books can be purchased second hand at the Guild Secondhand bookshop (second floor, Guild Village), which is located on campus.
  • Contact hours provide an indication of the type and extent of in-class activities this unit may contain. The total amount of student work (including contact hours, assessment time, and self-study) will approximate 150 hours per 6 credit points.