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       Sigma-algebras and measurable maps (Sætning 1.2, The Borel sigma-algebra, limits of measurable functions, rules for measurable functions).

B       The integral of positive functions (in particular, Lebesgue's monotone convergence theorem).

C       Uniqueness of the Lebesgue meaasure.

D       Density of C_c(R^k ) in L_p. (Sætning 7.28 and page 7.19).

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

A       Sigma-algebraer og målelige afbildninger (Sætning 1.2, Borel-sigma-algebraen, grænseovergange af målelige funktioner, regneregler).

B       Integral af positive funktioner (især Lebesgue's sætning om monoton konvergens).

C       Entydighed af Lebesguemålet.

D       Tæthed af C_c(R^k ) i L_p. (Sætning 7.28 og side 7.19).

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