I am currently in my $2^{nd}$ Year($3^{rd}$ Semester) of Undergraduate Statistics Degree. I am having a Probability III Course(The Syllabus is attached below) as a part of my curriculum. I am finding it little difficult to just follow the Lecture Notes provided by the Professor.
So, It would be really helpful if I can get some suggestions for study materials to follow alongside. It can be Video Lectures, Lecture Notes, Books, etc. I have decent knowledge of Real Analysis, which was a 2 semester course during my $1^{st}$ Year.
And any additional advice or problem solving materials or tips is also appreciated.
Many topics in advanced probability are actually just measure theory applied to probability spaces, i.e. to measure spaces where the whole space has measure one. Hence, a nice book on measure theory might come in handy. My favorites are:
(1) Real Analysis: Modern Techniques and Their Applications by G. Folland
(2) The Elements of Integration and Lebesgue Measure by R. Bartle
Now, for a more probabilistic approach, you can try e.g:
(1) Probability and Measure by P. Billingsley. I'd say this is a pretty complete and beautiful book, although it is probably better suited to graduate students.
(2) Probability: Theory and Examples by R. Durret. This one is easier to follow but a little brief at some points IMO.
(3) A Course in Porbability Theory by K. L. Chung.