What is the definition of "source population"? What is the definition of source population?
Suppose we screen $100,000$ people and then include $50,000$ people in three studies $A$, $B$ and $C$. For study $A$, is the source population the $50,000$ people or the $100,000$ people screened?
 A: The source population in an epidemiological context should be the group that you would like to make inferences about, based on what you see in your sample. 
A: The source population would be the one that the 100,000 people were drawn from - not necessarily only those 100,000 people. You say that these people were screened which I take to mean they were assessed in some way to determine eligibility to be a part of your sample of 50,000 people. There are then two possibilities that I can see: 
(1) these 100,000 people represent the entirety of the population about which you want to make inferences, in which case the 100,000 people are the source population for all three studies and the subset of the 50,000 people selected to be in each study is the study sample for that study. 
(2) these 100,000 people are a subset of the population about which you want to make inferences, and were selected in some way for screening. In this second case, the 100,000 people are not the source population - the source population is the population from which the 100,000 people were originally selected. This is true for all three studies. The 100,000 people can be considered a sample used for recruitment, and the subset of the 50,000 people used in each study is the specific study sample for that study.
A: The source population in your example is somewhat ambiguous - though a source population for any given study is often somewhat hard to define.
Generally speaking, the source population is the population from which your study subjects are drawn. In your example, that would be the 100,000 screened individuals under a specific assumption. Namely, that the screened population is an entire population.
For example, if your study screened 100,000 individuals in the U.S. Navy chosen at random, your source population is not the 100,000, but "Active duty members of the U.S. Navy". The smaller studies are just sub-sets of that 100,000 person group, but that's not the population you drew the study samples from.
I find the best way to think about the source population is to ask "Who could have been in my study?" Is there something about those 100,000 that means they're the only people who could possibly have enrolled, or is there a greater population out there that the 100,000 were themselves drawn from?
A: Rothman certainly implies that "source population" is just "population", in which case the source population would, I think, be the population from which the 100,000 people came. The 50,000 in each study is the sample. 
