Why do you say this?

A market segment just is a market according to the dictionary definitions. And legally, a lot of EU competition law concerns exactly how one individuates such markets/market segments.

Can you draw out what you're claiming more?

Not really as its very simple assertion. Apple do not have a monopoly. They control a segment of a rather large, and competitive marketplace. To say that they have a monopoly over their products is not a cogent statement as every manufacturer has such a 'monopoly'. The EU laws that you are referring to concern the abuse of a dominant position in a market, something which Apple as we are all too often reminded do not have.

The fact remains semantically and legally that you a monopoly of the segment or niche of a market is not possible. A company can be abusive (which is what you mean when you say monopoly - something which in and of itself isn't illegal), but unless they control the significant majority of the whole the it is legally not an issue. Morally is different debate.

> To say that they have a monopoly over their products is not a cogent statement as every manufacturer has such a 'monopoly'.

Well, I don't know what you mean by 'cogent', as that's generally taken to be a property of arguments and not statements (there may be loser notions, but as I say you'd need to spell out what one you intended). However, the statement that 'Apple have a monopoly over Apple products' is a true statement, which is all that matters to establish the semantic point. It might be trivial, but it's trivially true.

If I might try a helpful suggestion, it seems to me your confusion is arising because you're thinking something like 'if x is a market segment, then x isn't a market'. But of course that doesn't follow, as one can individuate markets at different levels (more or less fine grained).

"It might be trivial, but it's trivially true." It's trivial to the point of not being relevant. If the justice system were to punish every manufacturer that had a monopoly over their own product then nothing would get made. Cogent isn't perhaps the right word. As statements go "$megaCorp has a monopoly over their own products" is meaningless, yet it is constantly cited in these discussions as reason to pursue damages.

Look, there are several issues here. There's a narrow semantic point. On that point (which I think you explicitly denied), you can have monopolies over market segments. Personally, I like semantics, and think semantics is often less trivial then people suppose, but I accept others may be less interested.

Then there's a legal point about whether one opens oneself to legal action for dominance when operating in certain ways over market segments - I think it's also true you can be. But I'm not that advanced in my legal training, so don't take a strong position on that.

Further, there are normative and moral issues about what should be the law, and what one should do in these cases - but discussing those would take a long time...

If consumers face substantial barriers in switching to a rival then there might be an antitrust case. From the point of view of competition policy, the idea of "market for this" vs. "market for that" can be misleading

What barriers are they facing? As an owner of an Apple device, can they not sign up for Dropbox at all? Not being able to signup for a competing service that can involve a financial transaction is not anticompetitive if the consumer has other means, whit they do. Indeed if the consumer goes to the Dropbox website using Safari browser of their own volition, the can sign up immediately.

The issue here is one of sensationalism. As a community, we a far too quick to jump to the "$corp is evil!" conclusion without looking for a reason, however ridiculous it may seem. We, as a community, are too cynical for own good.