Mathematics - 13 December 2007

Let A be a subset of R^n with Lebesgue measure m(A) < oo. Let x + A be the translation of A by the vector x of R^n and define f:R--> [0, oo) by f(x) = m( A intersect (x + A)). Show that f is continuous.

My idea was to prove this first to nice sets like cells and then approximate A by a sequence of such nice sets. I tried to obtain a sequence of continuous functions converging uniformly to f, which would establish its continuity. But I got mixed up.

Is this aproach good? Can anyone help, maybe suggesting a different approach.

Thank you

2007-12-13 23:36:42 · 2 answers · asked by Steiner 7

2007-12-13 23:31:10 · 10 answers · asked by Jacob F 2

Can anyone help me how to solve this problem step by step. Please click on the link to see the problem. Thanks...

http://img528.imageshack.us/img528/697/18717776gk2.png

2007-12-13 23:17:19 · 4 answers · asked by David N 1

Find d/dx f(x) if we know that d/dx(f(3x))=x^2

2007-12-13 22:30:12 · 5 answers · asked by ---- 2

Do you go by the leading coefficient or the multiplicity..

Ex...3x^4+7x^3+x^2-7x-4

How many zeros...I got three (1, -1 and -4/3)...so does that mean we go by leading coef...basaically, how can u tell?

THANKS!

2007-12-13 21:39:56 · 6 answers · asked by Anonymous

ok, the given series is, summation 1 to infinity of (n^4 * x^n)/2(n-1)! and we need to find the radius and interval of convergence

the ! is the factorial symbol not me exclaiming... hehe...
ok so
an + 1/ an = absval.( (n+1)^4 * (x^n+1) / 2(n)! * 2(n-1)!/n^4 x^n )

absval. ( (n-1) (n + 1)^4 x / n^4 )
(1-1/n)(1+1/n) / 1/n (x)

and then what? what am i supposed to do with 1/n in the denominator.

2007-12-13 21:12:08 · 1 answers · asked by Rogue Bagel 2

Mameha adds two odd prime numbers together.

a) Construct an EBNF grammar for the sum that Mameha is going to obtain (assume there is no leading zero in the sum).

2007-12-13 20:59:14 · 1 answers · asked by Terry W 1

a) A = {x: x is a letter in the word 'mathematics"}
b) B = {x: 3x² - √20 x - 5 = 0, x is real numbers}

2007-12-13 20:48:25 · 1 answers · asked by matchamatics 1

lim (( ln (4+7x) - ln 4 ) / (e^4x -1)) ...ffrom the answer key: its 7/16
x->0
how do u do this in the case of a ln?
im confused please help

2007-12-13 20:05:56 · 3 answers · asked by jocuzzi 1

2007-12-13 19:42:43 · 2 answers · asked by abinash K 1

http://hotmath.com/help/bookindexes/cpm02/index.html#pid=cpm02_9_GM_Classwork_GM-18_332

please help, its due tomoroow

2007-12-13 19:32:05 · 3 answers · asked by citygirl9 2

f(x) = 3·ln(2x) - x/3 , x > 0.
Here find the derivetive's 0 point

2007-12-13 19:29:06 · 4 answers · asked by Anonymous

okie here are the problems and ps thx everyone!

1. find the gcf (greatest common factor) of 60, 72, and 36

2. find the gcf of 32, 48, and 64.

3. find the gcf of 36,48, and 30.

4. gcf of 28, 56, and 42.

5. 80, 110, 90.

6, last one, 9, 25 and 49

for everyone who gave me the correct answer thx! have a great night =)

2007-12-13 18:05:15 · 3 answers · asked by Anonymous

okie,
question 1......what are the greatest common factors of
12, 20, and 26
question 2 greatest common factors of 15, 20, and 25?
thx everyone!

2007-12-13 17:52:29 · 5 answers · asked by Anonymous

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.

2007-12-13 17:52:16 · 2 answers · asked by Anonymous

Find all relative extrema and points of inflection for

f(x) = x - sinx

over the interval
0

2007-12-13 17:39:21 · 2 answers · asked by Anonymous

2007-12-13 16:48:18 · 4 answers · asked by Sparticuz 3

I need help for an upcoming test, and can't seem to find help anywhere. Help is appreciated. thank you in advance

2007-12-13 16:47:06 · 4 answers · asked by Docta Procta 2

2007-12-13 16:42:30 · 5 answers · asked by Scythian1950 7

Ok the porlbmei s

1. 2x^2-6x+5=0
2. 2x^2-6x-5=0

It says we have to determine a nature of the roots..

i really dont get it how do you identify a nature of roots,
and also how many natures of roots are there?

2007-12-13 16:41:25 · 5 answers · asked by jin l 2

2007-12-13 16:30:01 · 3 answers · asked by Fred J 1

Jansen Electronics has four machines that produce an identical component for use in its videocassette players. The proportions of the components produced by each machine and the probability of one of that component being defective are as follows:

Machine 1- Proportion of components produced= .15 Probability of defective component= .04

Machine 2- Proportion of components produced= .30 Probability of defective component= .02

Machine 3- Proportion of components produced= .35 Probability of defective component= .02

Machine 4- Proportion of components produced= .20 Probability of defective component= .03

What is the probability that the component selected at random is defective?

* Our book only teaches us how to do the problem if they tell us what Machine we're using, not which one we're selecting at random...

2007-12-13 16:21:11 · 2 answers · asked by textfiend 2

Suppose x=3−4i is a zero of the function f(x)=x^4−6x³+29x²−24x+100 . What must be a factor of f ?

Any solutions are greatly appreciated :D

2007-12-13 16:06:30 · 5 answers · asked by nintendogamer91 4

Please hurry, i have only today to finish!

2007-12-13 16:00:38 · 9 answers · asked by PEACEMAKER_GREEN 1

2007-12-13 15:59:54 · 6 answers · asked by realchurchhistorian 4

2007-12-13 15:48:58 · 9 answers · asked by Anonymous

64 total candies 11 red, 18 orange, 3 yellow, 11 green, 12 blue, 9 brown. After I figure the perecents out I have to take each percent and graph it onto a pie chart. Yet, when you add the perecnts up they do not equal 100% so my pie chart is not even. How do I do this?

2007-12-13 15:48:57 · 5 answers · asked by Racquel B 1

how do you solve these:

1. 8cotx=-7 (between 0 and 360 degrees)
2. cscx=-12 (between 0 and 360 degrees)
3. sin(3x)=.8 (all real answers)
4. csc(x/4) = -square root 2 (between 0 and 2pi)

2007-12-13 15:40:08 · 3 answers · asked by heartsrstrongheadsrweak 1

Could someone post the answer to these problems and show how to do them please.... I don't have a clue about finding the missing sides.... help

http://www.mathhelpforum.com/math-help/trigonometry/24849-rationalizing-denominator.html

2007-12-13 15:22:15 · 1 answers · asked by ariesmarsgal 1

Yea... Eigenvalues and explanation of each step would be greatly appreciated.

2007-12-13 15:16:27 · 2 answers · asked by Aeacus 2