It is considered a live birth if the baby breathes - however I know of one case last year ( 2014 so far more recent) where the baby lived for half an hour but because he was born before viability (was 23 weeks) the doctor wouldn't sign a death certificate and said it was a miscarriage - which then meant the parents couldn't get a birth certificate either.
It is wrong, and there was a huge debate about it in a study day with me and a few others saying it was wrong and they should have had birth and death certs and others saying if born before 24 weeks then nothing (btw law is on our side and you should have both). But if the doctors back then also believed that too premature births didn't count you may end up with that situation.
I believe the cut off for viability in the 1930s was 28 weeks