Welcome to these probability Tutorials which in the long run, are meant to be a complete online course in probability theory. Unfortunately, in its present form, this website contains more real analysis, general topology and measure theory than actual probability. It is more about the foundations of probability theory, than probability itself. In particular, it is a very suitable resource for anyone wishing to study the Lebesgue integral.

These tutorials are designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved Theorems, as well as clear Definitions are spelt out for future reference. (An alphabetical index A|B|C|D ... should also be helpful.) Contrary to standard university lectures or textbooks, these tutorials do not contain any formal proof: instead, they will offer you the means of proving everything yourself. However, for those who need more help, Solutions to exercises are provided, and can be downloaded in A4 paper format from the Printing  page. 

If you fancy having a little break, have a tour round the History page where all the   mathematicians mentioned in these tutorials are presented to you. Notations used are described on the Notations page. If you wish to discuss anything about this site, you are welcome to join our Discussion group. There are also plenty of good sites to check out for on the Links page.

Finally,  if you are looking for a book, the following pages may help:

General Topology
Real Analysis
Measure Theory
Probability Theory
Finance

These are all books I own (with the exception of some financial ones). Needless to say, I haven't read them all, and most of them are in fact too advanced, so I don't undertand them... But they're still beautiful, so I warmly recommend them, and I hope to master more of them in the coming years, so I can write plenty of new tutorials :-)

Oh... one last thing: these tutorials would not be what they are without the corrections and improvements suggested by some as shown on the Error/Typos page. I am greatly indebted to them, and hope that others will follow suit. I am also greatly indebted to D.P. Story for his kindness and support, and having provided me wih his AcroTeX publishing format. Without him, these tutorials would not exist.

Good luck, and let me know how you get on!