Measure Definition and 1000 Threads

I am confused about the calculation of Hausdorff measure. On one side, the Hausdorff dimension is calculated as the point where the Hausdorff measure of the figure jumps from infinity down to zero (formally, in terms of limits of the inf and sup of the measures of the covers, etc.) But that...

I have an Antenna system using two patch antennas, and I'm trying to determine the SNRin and SNRout of the system. I'm trying to determine the noise figure - is there a way to do it using scattering parameters? Thanks!

Homework Statement Construct a low-pass filter and measure the gain (Vin/Vout) for a range of frequencies 20 Hz to 10 kHz using an oscilloscope. Plot your data along with the theoretical curve. Use a semi-log graph. What is the half power point for this filter? Does it match the theoretical...

Hi, I have to build a sensor circuit to measure temperatures up to 2000°C. I searched for an IR sensor for this and it seems they are very costly. Is there a way to suppress the incoming IR radiation from the source and direct it to a sensor having lower temperature sensing ranges? I...

Homework Statement A student needs to connect a voltmeter to measure the potential difference across the parallel resistors in the circuit shown below (http://www.bced.gov.bc.ca/exams/search/grade12/english/release/exam/0708PH_p.pdf ) Question 28 Homework Equations None The...

Hello again. I've got 2 simple questions relating to trigonometry in circular measure. I've got answers to both but they are not satisfactory. So here goes. 1) This question requires that we show that A (which is the area of a circle) is a maximum and not a minimum, when r=3/2. A=3r-r^2...

Homework Statement Hi, I have virtually no background in electronics and I have been given the following task. I have to measure the capacitance of the (real) circuit below (using labview, but it is the theory of how to do this that I am interested in). I am not able to use the...

Homework Statement Just got done reading the chapter... Want to make sure I have this right... IF Circumference = 2(pi)r Let cir = 360 deg. So that 360 deg = 2(pi)r And 180 deg = (pi)r IF r = 10 then 180 = (pi)10 Hence half of a cirlce with radius of 10 has an arc measure of...

It is often stated that the one way speed of light cannot be measured and that the isotropic speed of light is just an assumption based on two way measurements and clock synchronisation conventions. Here is a proposal for measuring the one way speed of light. It is not entirely original as it...

Homework Statement Here's an old qualifying exam problem I'm a little stumped on: Let (X,\mu) be a \sigma-finite measure space and suppose f is a \mu-measurable function on X. For t > 0, let \[ \phi(t) = \mu(\{x \in X : |f(x)| < t \}). \] Prove that \[ \int_0^{\infty}...

Homework Statement Is there any non-Lebesgue-Measurable set A in R such as A contains all rational numbers? Homework Equations The Attempt at a Solution I've tried assuming that this is true... If such a set exists, then both A and A^c aren't countable... I've tried looking at A^c...

have a manometer. i want to measure the static pressure for calculation of axial flow fan efficiency. please tell me how would i do it. Regards.

Homework Statement Let A \subseteq R be a Lebesgue-Measurable set. Prove that if the Lebesgue measure of A is less than infinity , then the function f(x) = \lambda(A \cap (-\infty,x)) is continous. Homework Equations The Attempt at a Solution I'm really confused about the definition of...

Homework Statement Prove the set A= \bigcup_{n=1}^{\infty} ( \frac{n}{5} , \frac{n}{5} + \frac{n+1}{2^n} ) is Lebesgue measurable and calculate its measure. Homework Equations The Attempt at a Solution I've proved the set is measurable...But how can I calculate its measure? I...

While posting a reply in another thread, I had an inspiration for a device to measure spacetime curvature. It is well know that we can measure this curvature by measuring the angles of a large triangle or comparing the circumference of a circle to its radius, but his device may may be simpler or...

Measure the electric field? Anybody can tell me how to measure the electric field in a microwave plasma ? The method? The theory?

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.

My professor gave this function in class as an example (for Fubini's Theorem) f : [0,1]² -> R defined as: f(x,y) = 1 if x not equal to 1/2, 1 if x = 1/2 and y rational, and 0 if x = 1/2 and y irrational. My professor said that this function is Riemann integrable since the set of...

what is the best method to measure gravitational redshift using a small telescope ? and in which stars the effect is the strongest ?

Homework Statement If E has finite measure and \epsilon>0, then E is the disjoint union of a finite number of measurable sets, each of which has measure at most \epsilon. Homework Equations The Attempt at a Solution I proceeded by showing that by definition of measure, there is a...

Hello, This is my problem: I have a network analyzer, that is capable of measuring the S-parameters of a 2 ports network. Let's say that I connect antenna #1 (a standard half-wavelength dipole) to port #1 of the NA, and antenna #2 (same type of dipole) to port #2 of the network analyzer...

An observer is standing right outside of a charged capacitor. Can he feel a negative or positive (or both) charge from the plate?

For a science investigation, I want to investigate how different factors affect the resonant frequency of wineglasses, however, I need some way to measure the frequency quantitatively. Is there some kind of computer program that can do so through the computer microphone? And if so, would the...

Hey i'm given a measure on $\Omega =\mathbb{N}, A \subset \mathbb{N}$ and should check additivity as well as $\sigma$-additiviy. Additionally i should give an example for a set where $\mu(A)$ is not defined: $\mu(A)=\lim_{n \rightarrow \infty} \frac{1}{n} \xi\mid _\mathbb{N} (A \cap...

Do we essentially measure its wavelength and calculate the frequency? I thought we figured out frequencies by refracting the light into its many frequencies - (ie, like we see when looking at a Doppler shift). But, refraction formulas are based on VELOCITY, not wavelength and light travels at...

Homework Statement [PLAIN]http://www.album.com.hk/d/1546698-2/Untitled-1.jpg Homework Equations Every measurable set in R can be written as a difference of Gdelta set and a set of measure zero. Every open set in R is just a countable union of disjoint intervals. The Attempt at a...

Why do we measure the angle of incidence or reflection (or say refraction even) w.r.t normal to the surface and why not w.r.t the horizontal surface?

Hello all, I have a few questions in my mind: 1) \lim_{n\rightarrow \infty}[0,n) = \cup_{n\in\mathbb{N}}[0,n) = [0,infty) holds, and for \lim_{n\rightarrow \infty}[0,n] = \cup_{n\in\mathbb{N}}[0,n] = [0,infty) is also true? It should not be [0,infty] , am I correct? 2)...

see the pic [PLAIN]http://store2.up-00.com/Oct10/opW54159.jpg

Hey guys, below is a small question from introductory measure theory. Maybe be completely wrong on this, so if you could point me in the right direction I'd really appreciate it. Claim: Let B=\mathbb{Q} \cap [0,1] and \{I_k\}_{k=1}^n be a finite open cover for B. Then \sum_{k=1}^n m^*(I_k)...

Homework Statement Let (X , M, m) be a certain measure space and {En} sets in M with the property: \underline{lim} (Ek) = \overline{lim}(Ek) = E prove that lim m(Ei) exists and = m(E) as n approaches infinity. Homework Equations The Attempt at a Solution i solved the problem...

Is there a "standard" probability measure one would use for the set of smooth real-valued functions on [a, b]? My intuition is picturing a setup where you cut out shapes in the x-y plane, and then the set of functions whose graphs are contained in that shape have a measure proportional to the...

This is a pretty elementary question but I had it on a quiz and it made me think... does a speedometer measure a scalar or vector quantity? I answered that it measures a vector quantity my rational being that it is the instantaneous speed in a forward direction, always. It doesn't matter if...

On this webpage http://www.mathpages.com/home/kmath241/kmath241.htm" are these words of Maxwell: "The only practicable method of determining directly the relative velocity of the aether with respect to the solar system is to compare the values of the velocity of light deduced from the...

Dear all, I have a piece of brass material at high temperature (around 300 Celsius) and I would like to know how can I measure the heating power stored by this piece. the piece is designed in a way that we can flow a fluid through it. For low temperatures ( below 100 Celsius) it is maybe...

Homework Statement Show that there is a continuous , strictly increasing function on the interval [0, 1] that maps a set of positive measure onto a set of measure zero Homework Equations The Attempt at a Solution I need to find a mapping to a countable set or cantor set but I...

Is the integral over a set of measure zero always equals to zero? Can the integral be undefined?

Hi, How can I measure the capacitance of a capacitor, using the following: a battery, a digital voltmeter (which records voltage as a function of time), a digital ammeter (which records current as a function of time), an industrial capacitor, two copper plates, and several...

Homework Statement Let (R, \mathcal{B}, \mu_F) be a measure space, where \mathcal{B} is the Borel \sigma-filed and \mu_F is the Lebesgue-Stieljes measure generated from F(x) = \sum^\infty_{n=1}2^{-n}I(x \ge n^{-1}) + (e^{-1} - e^{-x})I(x \ge 1) Use the uniqueness of measure extension in...

If we have two red balls and we are to choose one it is true that the probability measure of picking a red ball is 1. In this case it is understood that the sample space only contains a red ball and this is because events in the sample space are to be disjoint. But how come this is not the...

If I squeezed someone with a hug, how would I measure the force

Homework Statement Show that if a set E has positive outer measure, then there is a bounded subset of E that also has positive outer measure Homework Equations We can take an intersection of E with some of its covering sets. This will give us a subset of E, but how can we be sure...

Hi all I am struggling to see the difference between Convergence in probability and Almost surely convergence of a sequence of random variables. From what i can see Almost surely convergence of Sequence of Random variables is very similar to pointwise convegence from Real analysis. I am...

Homework Statement Let A and B be bounded sets for which there is \alpha > 0 such that |a -b| \geq\alpha for all a in A and b in B. Prove that outer measure of ( A \bigcup B ) = outer measure of (A) + outer measure of (B) Homework Equations We know that outer measure of the union is...

i have no idea of how to measure a berry phase take a 1/2 spin in an external magnetic field it is well known that this system can exhibit berry phase if the external magnetic field B takes a loop on the sphere. but how to measure the berry phase? how to separate the berry phase from...

Homework Statement In a triangle, two sides that measure 6 centimeters and 10 centimeters form an angle that measures 80 degrees. Find to the nearest degree, the measure of the smallest angle in the triangle. Homework Equations A2 = B2 + C2 – 2bc Cos A The Attempt at a Solution...

In general, on earth, angle is easier to measure with a reference point, but what about measuring something in space (with no reference point?)

Hi all, I was thinking about measuring the temperature of an arc discharge. The size of the discharge is very small, in the order of micrometer. So it is not possible to put a thermocouple near the it. Thank you very much.

hello people can anyone help me...? here is my objective... To measure how long a person stays on the air, when it jumps, until it reaches the ground at the same position. Given: Weight of the person Force exerted Find: Time Height of the jump ...plsss

Homework Statement Find the integral of the function f(x)=3 when x is rational and 2 when x is irrational on the interval [0,1]. Homework Equations The Attempt at a Solution So I partition [0,1] into two disjoint sets A and B. A=[0,1] \cap Q and B=[0,1] \cap Q^{c}. Now the...