noam

8mo10

Though now that I think about it, if the difference is some **irrational** number then this seems to work, as any set would contain exactly one unique rational number. Now they each have the cardinality of R, and the family has the cardinality of Q. And then it all seems to work.

Does that seem right?

8mo10

I fail to see why the family of sets is countable. if is of cardinality , which I totally agree about, then how can a union of a **countable** family of them which is basically be equal (0,1)?

8mo21

What do you mean by "no reasonable σ-algebra can encompass the full power set"? The power set is the biggest σ-algebra of a set, but what set? And what is "reasonable"?

8mo21

Found a typo:

Definition 2.2. Let be a metric space. We say that a functional is k-Lipschitz

continuous if there exists such that for all . In

such a case k is called the Lipschitz constant of f.

I think it should be: instead, as while .

Can someone break Definition 1.1 down for me? I got lost in all the notation and what acts on what, what is projected to where..