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I believe monopoly laws should apply to any companies having a "few million" customers and it not being trivial for customers to switch or there not being much choice to switch to.

In case of Apple it's neither trivial to switch (you can't move bought apps over) nor is there much choice (in practice it's basically Apple or Google).

I have thought pretty hard about the need to include a fuzzy word like equivalence in my definition of monopoly, what would it take for me to persuade you to adopt my definition?

By that logic, wouldn't any company inventing/developing a new technology be forming a monopoly?

Yes.

Monopoly laws should be updated to reflect the digital era of today.