There is nothing too special about this list - in fact it is based on the Holley list. I include some Royden problems and I also say which problems I felt were key going into the exam. These were problems I did repeatedly and extracted as much out of as I possibly could. The categorization is not intended to be week 1, week 2, etc as some topics appear with greater frequency as others. Here is the list:

Measurable sets

Key Problems

p64 #14 / Jan93 #6 / Aug95 #5
Aug92 #2
Aug95 #1
Aug97 #1

Other Problems

Jan99 #2
Jan00 #4
Aug90 #6

Measurable functions, Egoroff, convergence in measure

Key Problems

p71 #24
p71 #28
Aug91 #1
Jan94 #1
p73-4 #30, #31 / Aug02 #6

Other Problems

Aug93 #7
Aug94 #4
Aug96 #2
Jan01 #1
Jan89 #3

Integration, convergence theorem applications

Key Problems

Jan90 #7
Aug92 #1
p93 #15, #16 / Aug02 #7
Jan95 #2

Other Problems

Aug90 #2
Jan93 #5
Jan95 #7
Aug95 #2
Jan98 #5
Jan99 #3, #7
Jan00 #5
p89 #7
p94 #17

Absolute continuity, bounded variation, convexity

Key Problems

p112 #20
P104 #10 / Jan97 #1
Aug95 #3

Other Problems

Jan92 #2
Aug92 #2, #4
Jan94 #2
Jan98 #6
Jan00 #2, #3
Jan01 #2
Jan02 #3
Aug02 #4
p104 #8
p111 #15, #16

L^p problems

Key Problems

p127 #17 / Aug91 #3
Jan92 #1
Jan95 #5 / p119 #2
Jan96 #2 / p126 #16
p127 #18
p123 #8

Other Problems

Spr84 #1
Jan88 #3
Jan90 #3
Aug92 #5
Aug96 #5
Jan97 #2
Aug99 #1
Aug00 #3
Jan01 #5, #6
Jan04 #5
p126 #11

Integration, Fubini-Tonelli, Radon-Nikodym, product measure

Key Problems

p312 #29
Fall87 #1
Aug91 #2
Jan96 #1

Other Problems

Aug88 #3
Jan90 #6
Jan92 #3
Aug00 #6
Jan01 #4, #5
Aug01 #7
Aug02 #3

Baire, Ascoli-Arzela, Stone-W, miscellaneous

Jan90 #2
Aug91 #6
Jan92 #5
Aug92 #3
Jan94 #6
Jan96 #3
Aug96 #3
Aug98 #3
Jan99 #5, #7
Aug01 #3
Aug02 #1
Jan02 #2
Jan04 #2
p161 #31-37
p303 #17
p170 #50