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Aug
9
reviewed Approve How to solve this IVP?
Aug
9
comment Do the radii of a family of nested balls (in a Banach space) converge?
That's interesting and surprising for me, many thanks. Can I ask you which is the problem for $\mathbb Q_p$, thus? Why does Henning Makholm's proof below does not apply in thi case? I am not very familiar with $p$-adic numbers, to be honest. Thanks again for your comments.
Aug
9
comment Do the radii of a family of nested balls (in a Banach space) converge?
@you-sir-33433 Sure, thanks for pointing it out; but if you are in a Banach space and the balls are nested then necessarily the intersection is not empty.
Aug
9
comment Outer Measure is not Finite Additive
You may find this interesting. math.stackexchange.com/questions/878962/…
Aug
9
accepted Do the radii of a family of nested balls (in a Banach space) converge?
Aug
9
comment Do the radii of a family of nested balls (in a Banach space) converge?
Oh, I see your point. Thank you very much for the kind and fast reply.
Aug
9
asked Do the radii of a family of nested balls (in a Banach space) converge?
Aug
9
comment Nested sequences of balls in a Banach space
Sorry for this comment which is probably stupid but I am wondering how you would prove that $B_r(x) \subset B_s(x)$ implies $r \le s$. What about these examples: math.stackexchange.com/questions/734248/… ? Thanks.
Aug
8
accepted A strictly convex function defines an implicit function with non-positive second derivative
Aug
7
revised Jordan Measure and Lebesgue Measure
edited title
Aug
6
comment How do I approach the problems asking about uniqueness
@user86418 Oh, sorry: you are perfectly right, I have been stupid. Thanks for pointing it out, now it makes sense.
Aug
6
comment How do I approach the problems asking about uniqueness
The solution of the first problem is straigthforward if we do not ask for periodicity (just take $C(\mathbb R)$ with the sup norm and verify that the "obvius" map is 1/2-Lipschitz: then apply Banach-Caccioppoli fixed point theorem). I am wondering what changes adding periodicity condition: the space of continuous periodic functions is still complete under the sup norm hence I think that the same argument applies.
Aug
5
revised A strictly convex function defines an implicit function with non-positive second derivative
Added a possible solution to new doubt
Aug
5
revised A strictly convex function defines an implicit function with non-positive second derivative
Added a new doubt
Aug
4
comment A strictly convex function defines an implicit function with non-positive second derivative
This is nice, thank you for your answer. I have been very stupid because I did not notice that. Thanks again. By the way, what do you think about the first point? Is it correct? I am now doubtful because I have proved only that the difference quotients are $>0$, maybe when we pass to the limit we get $0$... Thanks.