The written exam consists of two parts. The first 90 minutes are without any means of help ("closed book") and during this time an Essay Problem is do be finished and handed in. Here, one typically is asked to state and prove one or several specific propositions and theorems in a central topic from the course. In the remaining 90 minutes more traditional problems are to be solved, and here all usual means of help are allowed ("open book").

The essay problem will be one of the following 5 problems. Notice that a Danish translation is appended.

A       Measure (derivation of properties held by a measure, examples, almost everywhere).

C       Uniqueness of the Lebesgue meaasure.

B       Product measures (Sætning 6.6, Lemma 6.7, and a description of the product sigma algebra).

D       Fischer's completeness theorem.

E       The Fourier transform and the Schwartz functions; in particular Sætning 8.6 and Sætning 8.8.

A       Mål (udledning af egenskaber ved mål, eksempler, næsten overalt).

C       Entydighed af Lebesguemålet.

B       Produktmål (Sætning 6.6, Lemma 6.7 og omtale af produkt-sigma algebraen).

D       Fischer's fuldstændighedssætning.

E       Fouriertransformationen og Schwartzfunktioner; specielt Sætning 8.6 and Sætning 8.8.