baire class

[amy666]

give a simple example of a function of baire class 5.

regards

tommy1729

[Dave L. Renfro]

amy666 <tommy1...@hotmail.com> wrote:

> give a simple example of a function of baire class 5.

Any constant function works if you use the current "inclusive"
definition of the Baire classes. As for the older "non-inclusive"
definition of the Baire classes . . .

When Baire defined "Baire functions" in his 1899 Thesis,
Baire gave an example of a Baire 2 function that isn't
Baire 1 (apparently due to Volterra, according to a comment
Baire makes in paragraph 38 on p. 44 of [1]). The last few
pages of Baire's paper (pp. 44-48) give an explicit construction
of a Baire 3 function that isn't Baire 2, the first such that
appeared in print. The Russian L. V. Keldych gave an explicit
construction of a Baire 4 function that isn't Baire 3 sometime
in the late 1920's (apparently unpublished, but it's in Luzin's
1930 book), and then in 1940 (see [2]) she published a short
paper that gave explicit examples of Baire n functions that
are not Baire n-1 for each integer n > 1.

[1] Volume 30 (1906) of Acta Mathematica, pp. 1-48.
http://books.google.com/books?id=POQOAAAAIAAJ

[2] Keldych, C. R. Acad. Sci. URSS (2) 28, 675-677.
[JFM 66.0206.02; MR 2,256e]

Dave L. Renfro

[amy666]

>
> [1] Volume 30 (1906) of Acta Mathematica, pp. 1-48.
> http://books.google.com/books?id=POQOAAAAIAAJ
>
> [2] Keldych, C. R. Acad. Sci. URSS (2) 28, 675-677.
> [JFM 66.0206.02; MR 2,256e]
>
> Dave L. Renfro

sigh.

i want to discuss the topic on sci.math.

not some reference to dead mathematicians and dates or books i have to buy or dont have access too.

this happens way to often on sci.math.

its sci.math , not sci.reference or sci.amazon

regards

tommy1729

[G. A. Edgar]

In article
<29025605.107001.1242386...@nitrogen.mathforum.org>,
amy666 <tomm...@hotmail.com> wrote:

I thought Dave's post was exactly right.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/