anymore=lately

[Munch]

It’s called the “positive anymore” and wikipedia has a short article about it with some links if you are really interested.

But it is not standard English and if you use it almost everyone will think you are just making a mistake.

[ostap77]

If there is a rule you can apply, I can't imagine what it might be, but I'm pretty sure it isn't that. I can say it means something more like "these days" than "lately". Your example didn't work partly because "I've been working out" is complete already. Like I said, the use is unusual here and impossible most places, so don't kill a lot of time on it.

If I I say "I've been working out lately or these days", this might well mean that I started in the past, continued doing it up to the moment of speaking and may go on doing it in the future?

[Coolfootluke]

If I I say "I've been working out lately or these days", this might well mean that I started in the past, continued doing it up to the moment of speaking and may go on doing it in the future?

I would say that "these days" is wrong there. "I've been working out lately" is normal English, and I think you have the right idea about it. It does indeed imply that you intend to continue, at least for the immediate future.

In case you've forgotten, I am not a teacher.