I actually did not realize there was a name for this, so I proved and implemented this from scratch:

```
def random_subset(iterator, K):
result = []
N = 0
for item in iterator:
N += 1
if len(result) < K:
result.append(item)
else:
s = int(random.random() * N)
if s < K:
result[s] = item
return result
```

With proof near the end.