5
$\begingroup$

My question is about functions of bounded variation (BV) on the reals.

On one hand, Helly's selection theorem provides (fairly restrictive) conditions under which a sequence of BV-functions has a sub-sequence that convergences to a BV-function.

On the other hand, if a sequence of BV-functions converges to some function, then the latter is at most Baire 2.

My question is whether we can significantly improve 'Baire 2' in the previous, e.g. assuming the BV-functions in the sequence are uniformly bounded?

Improve this question
$\endgroup$
0

1 Answer 1

Reset to default
3
$\begingroup$

I happened across the following paper:

Charles Tucker, "Limit of a Sequence of Functions with Only Countably Many Points of Discontinuity", Proceedings of the American Mathematical Society, Vol. 19, No. 1 (Feb., 1968), pp. 118- 122, MR219029, Zbl 0157.20302.

The following theorem (statement at p. 118, proof from p. 120 to p. 122) expresses that pointwise limits of regulated functions are equal to a Baire 1 function outside of some countable set.

enter image description here

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .