Biostatqual

Hi I am in my 2nd yr of doctorate program in Biostat in a top 20 US institute. I took my written quals last yr and did not get through. I have my 2nd attempt in 3 months and want to get though this time. Last time I struggled with large sample theory; not much has changed this year. Still struggling with proofs like show X_n+Y_n converges as/p to x+y if x_n converges to x(in p/as) yn converges to y(in p/as). Basically need help on how to get better in measure theory proofs. Showing convergence for increasing and decreasing sets and so on.