Recent content by hermanni

OK, I got the idea of construction, thank you very much. (*) Do you think boundedness is one of these properties? If so, how can I show?

Well, I'm using the same definition and you're right, I didn't read carefully and 1/1-x is convex.

OK, my functions f and g are defined on [0, ∞) and I needed finiteness of number of intersections in [0, 1). They're both bounded, concave, increasing and BOUNDED on [0, ∞). I have now boundedness, can I claim finite # of intersections on [0,1)? I think I can do it for [0,1] based on what you...

and it's not a homework question but I need it as a part of an bigger argument :)) . AlephZero, your last line made me wonder : As far as I get, the domain is also important here. What if f, g : [0, ∞ ) \rightarrow ℝ, can we claim they intersect finitely many times in [0,1) ? Here I guess...

Alephero, can you explain that last line (maybe give reference )? Also I think here being increasing is also important , I think only concaveness is not enough here.

Hi all, I have a question. Suppose f : [ 0, l) \rightarrow ℝ is concave , increasing and continuous where l < ∞ and g : [ 0, l) \rightarrow ℝ is also concave, nondecreasing and continuous on the same interval. Can we claim that f and g intersect finitely many times in this interval (possibly...

Hi all, I have the following question: Suppose f: [0, ∞) \rightarrow ℝ and f is concave , nondecreasing and bounded on [ 0, ∞) . Does it follow that f is continuous on [ 0, ∞) ? Thanks in advance, H.

Actually no , in the course we only saw that if we have a premasure on a semiring , then we can extend it to a measure on the ring. Also we noted down If E \in S and F \in S then there exists a finite number of mutually disjoint sets C_i \in S for i=1,\ldots,n such that E...

Hi, I showed approximations for intervals. Can you give me an idea how I can show it for any set?? Regards, hermanni.

Ok , here's our course's definition : Let F be a right-continuos and nondecreasing function. Then lebesgue - stieltjes measure associated to F is u and: u(a, b] = F(b) - F(a) For the compact sets , we do approximation from inside .The thing that bothers me is extension from a semiring to the...

I need to show that any lebesgue stieltjes measure is a regular borel measure. I'm really clueless , can anyone help?? We know the definition and facts about the distribution function , how can we conclude approximation by compact or closed sets?? Regards, hermanni.

Give an example of a collection of functions f_n (x) for 0 < n< infinity each measurable but such that lim sup n->infinity f_n(x) is not measurable. I think , this collection shouldn't be a sequence of functions otherwise lim sup would be measurable. So I tried with sup first: Take V as...

Actually I didn't . The theorem says fn and f have the same number of zeroes, I don't understand how we supposed to use it.

Hi all, I'm trying to solve this question , can anyone help?? Suppose that D is an open connected set , fn ->f uniformly on compact subsets of D. If f is nonconstant and z in D , then there exists N and a sequence zn-> z such that fn ( zn ) = f(z) for all n > N. hint: assume that...

Thanx a lot guys , I solved the problem :))