Graduate Course in WEAK CONVERGENCE OF PROBABILITY MEASURES (6 Credits)

                         (Second announcement)

As earlier indicated (First announcement 16 October), I will give a course 
on this subject, following (and this time I really quite mean "following") 

BILLINGSLEY: CONVERGENCE OF PROBABILITY MEASURES, Second Ed., Wiley 1999. 

The start of the course has been slightly delayed, since several students 
told me that they intend to participate, but would like to finish integra-
tion theory (9 February (Math. Dept.)), before taking up weak convergence.

A look at the schedule for graduate courses at Math. Stat., reveals that 
there are three courses running already (January-March), but not a single 
course after that (April-May (June)). Just to make sure that mid February-
April (say) really is the right time slot for Weak Convergence, and that, 
for example, mid March-May (say), or April-mid June, is not better, I 
would like to make a short preliminary enquiry about this issue.

Hence I ask students who agree with the present time for course, mid Febr-
uary-April (say), should email me that preference, while students who 
prefer letting course run mid March-May (or April-mid June), should email 
me that instead. Especially, students for whome it is crucial (e.g., for 
their very participation in course) that one of the timeslots is used, 
rather than the other, should point that out. Please also indicate if it 
is the intention to follow both the topology part of the course (see be-
low) and the "main course" (Billingsely), or only one part (and which). 

Students for whome it does not matter when course is given needn't answer, 
if they don't want to. Obviously, such students are wellcome anyway later.

The enquiry is not decisive in itself (naturally there are disadvantages 
with changing agreed schedules), but will be used in an "advisory manner", 
as wisely as possible. 

The course will be preceeded by a two-to-three week long introduction to 
Topology. The introduction will be in the spirit of part I of Simmons 
well-known classic text-book. However, compared with what is covered by 
him, most set-theoretic things (Zorn's Lemma etc.) will be skipped, as 
will most topics in general (non-metric) topology that are not relatively 
immediate extensions of the corresponding metric results. What remains is 
what is needed for the study of Billingsley, together with additional mat-
erial, that "knit things together", and is a basic part of standard mathe-
matical (math.stat.) "jargon", even in quite basic graduate text books.

It is not really necessary that the introduction is immediately followed 
by the main course, but this is the most natural way to do things.

It is estimated that the topology introduction will give two credits, and 
the Billingsley course five-six credits. The manner in which grading will 
be carried out depends on how many students there are. I think it is vital
to encourage "active students", albeit this can hurt a bit when there are 
many other things to do. So it is likely that the grading will be a "con-
tinuous procedure" during the course, either with exercise sessions, or 
with "hand ins". However, we could have "hemtemta" instead, if prefered.

A necessary prerequisite for the course is Lebesgue integration. Except 
for that, I do not think there is any reason to stay away from the course, 
because of lack of preparation. (In fact, I strongly advice and encourage
everyone who has Lebesgue integrated to take the course.) 

Weak convergence is one of the most fundamental and basic things in prob-
ability. No probabilist can do really well without it. In fact, it used to 
be a mandatory course for graduate students with a probabilistic profile, 
at least in Lund. Even for quite practically oriented students, it should 
be considered among the most basic theoretical courses, after integration.

When I gave course previous time, ten years ago, I had only five students. 
But they are now all teachers at Swedish universities (one professor and 
three lecturers/docents in Lund, and one lecturer/docent in Växjö.) So 
this course is a must if planning for a future at universities.

If course should run as originally planned, starting mid February, I will 
announce date for introductory meeting, to decide about times for lectures, 
as soon as I have had ample response to this email (indicating that mid 
February is best time to start). This could be next Friday, at earliest, or
more realistically, the Monday after that (to give people time to return 
from Coal Holidays).

Best regards and wellcome, Patrik Albin