Python multiprocessing safely writing to a file

I am trying to solve a big numerical problem which involves lots of subproblems, and I’m using Python’s multiprocessing module (specifically Pool.map) to split up different independent subproblems onto different cores. Each subproblem involves computing lots of sub-subproblems, and I’m trying to effectively memoize these results by storing them to a file if they have not been computed by any process yet, otherwise skip the computation and just read the results from the file.