I was reading an article in which they are mentioning this sentence:
"sequence is equidistributed in [0, 2]"
where the sequence in question, is a sequence of real number (the article in question is the article of Wikipedia on equidistributed sequence). The equations are a bit hard for me to understand (but I am trying to decipher them) but I have two questions:
my understanding is that "equidistributed" doesn't necessarily mean "exactly evenly distributed". But like with the stratified sampling method, the space or interval over which the sequence is defined can be divided into even parts and "samples" can fall within these parts with some random variation on where they are exactly located within these parts. Would that sequence still stand as being "equidistributed" (in other words it's more or less regularly spaced) or does the term "equidistributed" imposes the samples to be exactly evenly spaced.
What does [0,2] mean? I have seen it in some papers now, but can't find an explanation on what it is. Any reference of things i could read on this would be great.
Thank you.