Measure Definition and 1000 Threads

I have been trying to learn some measure-theoretic probability in my spare time, and I seem to have become a bit confused when it comes to defining a probability measure on a sequence of random variables (e.g., the Law of Large Numbers). Most texts start by defining a random variable X{i}...

Just curious, what would be a means of measuring various frequencies of music? Obviously you would require a microphone, and then what? Would you need a specific type of software? What are the types of physics that would be involved... Would anyone be able to refer me to some notes or...

Hi, I have a question. Suppose I have a motor that runs on 3 phase power. If I only wanted to find out the total amount of current that the motor draws, how would I go about doing that? Would I just use a clamp meter to get the amount of current going through each phase and then add them up...

I have just now seen an advertisement on tv that claims to save up to 40% on residential water bills by inducing the meter to not measure the volume of air bubbles represented by entrained air in the supply line. This device is to be placed immediately DOWNSTREAM of the meter and presumably...

I need a simple way to measure the Solar Constant in a cold environemt (Norther Hemisphere, this time of year ;) ).While its easy to think of ways in which the Sun can heat up something for you...putting for example a bottle filled with water colored black due to ink dosen't seem like a good way...

I've been given a project to improve the design of a turbine used to measure the flow of beer! I've trawled the web and libraries to find previous work in the hope of finding some handy pointers, rules of thumb and simple equations to guide me. However, I've had little joy. Basic parameters...

Assume f > g two measurable function on [a,b] and E={(x,y) : g(x)≤y≤f(x), x ∈ [a,b]} Show ∫ (f-g) dm = m×m E . that m is lebesgue measure. (limits of integration is a,b) help will be appreciated so much

Hello, I've got a question about distance measuring via radio. I would like to measure the distance between two devices, relatively small ones, using radio and my question is how fine that measurement can be? The devices would be a maximum of say 15 metres apart and a preciseness of about a...

How do they do it? They need to know this to determine optimum braking temperature in order to have best performance braking. Yet, how do they do it? Measure it optically?

does the Dirac measure still exist with complex variance? The Dirac delta function can be rigorously defined as a measure. See http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure For the gaussian form of the Dirac delta function we have, \[ {\rm{\delta (x - x}}_0 ) =...

temperature is the measure of average kinetic energy of the molecules of a gas , also temperature is the measure of hotness or coldness of a body , but how does this molecular motion motion produce heating effect that we can feel?!

I want to mount some type of measuring device on a remote control car, and then crash it into a wall. As a result of the impact, I want to look at the speed the car was traveling at point of impact, as well as the rate of decelleration that occurred after impact (using various bumpers). I think...

Do you base your self-worth on the career path you choose , do you measure your self-worth by how productive you are in comparison to members of the rest of society? Do you measure your self-worth based on how many new friends you are able to attract or how many friends you possesses now ? Do...

One possible definition of measurability is this: A set E \subseteq \mathbb R^d is (Lebesgue) measurable if for every \epsilon > 0 there exists an open set \mathcal O \supseteq E such that m_*(\mathcal O \setminus E) < \epsilon. Here, m_* indicates Lebesgue outer measure. Apparently, an...

Is it true that a function is Riemann integrable on a bounded interval only if it's equal to a continuous function almost everywhere? I'd imagine this is the case, given the Riemann-Lebesgue lemma, which says that a function is RI iff its set of discontinuities has measure zero. (So the...

Where can I find an On-line exposition of the undefined nature of the measure in the Feynman path integral? Thanks.

When are two or more measures said to be measure theoretically equivalent? I have spent sometime on searching it; I am not getting it. Please someone help.

Hello, My 7th grade son has selected a science project which requires to find the impact of two toy cars crashing as part of the larger project. To keep it simple, he will keep one car fixed (i.e. not moving) and the other car crashing into the fixed car at varying speed. I have suggested...

meaning of "vanishes outside a set of finite measure" What does it mean when we say that a function vanishes outside a set of finite measure? As in the definition of the integral as a prelude to the Lebesgue integral in Royden's Real Analysis, 3rd ed. (p. 77). It said: If \phi vanishes...

Hi I have a question about Lorentz invariant measures, consider an integral of the form: \int d\mu(p) f(\Lambda^{-1}p) where d\mu(p) = d^3{\bf p}/(2\pi)^3(2p_0)^3 is the Lorentz invariant measure. Now to simplify this I can make a change of coordinates \int d\mu(\Lambda q) f(q)...

In Cadence we built a CMOS inverter. I made a transient response graph showing the input and output voltage waveforms. We're supposed to measure rise delay and fall delay of the output voltage. How do I do this? I heard from someone else that it's where the graphs cross 1.5V, but I'm still...

Hi all! It's my first post, but I follow this forum since a couple of years. Now I have a big question for you: how to measure the CDM (or \LambdaCDM) power spectrum (better, the variance \propto k^3 P(k)) from the observations? What parameters are necessary?

I'm not completely familiar with measures yet, but am trying to be. I'm trying to show a that a few sets in Rn have measure zero and am having difficulty showing this using countable covers with a total volume less than \epsilon. Is there an easier way to show that a set has measure zero? If...

Can a wheatstone bridge be used to measure very high resitances with good accuracy? If not what problems interfere?

Question about measuring observables. If have 2 particle system the particle seperation Q=x1-x2 and total momentum P=p1+p2 are observables of the system as a whole and are commuting. How do you measure these observables. It would seem the only way to measure the separation is to measure the...

Hi guys, I'm new to the physics world and am getting a bit confused with some of the terms used, stopping me getting the maths i need. Essentially I need to measure the deflection at the end of a beam, supported at one end. Like this...

I have a brass rod with a 90 degree bend. I want to measure the outer and inner radii by placing a piece of string along both of them, and then straightening the string out to determine the linear measurement. Is this an accurate method?

Im currently enrolled in embedded systems (so bare with me, I am not too experienced) and we had to come up with a final project for ourselves. Well, I would greatly appreciate some help in understanding some concepts of DSP. I am working with the freescale DEMOACKIT with the coldfire...

Homework Statement Suppose X is a subset of R such that its complement has Lebesgue measure 0. Show that there exists a c such that for all integers n, c + n is in X. The attempt at a solution I've been thinking about this for a while and I just don't see how such a c could exists. Any tips?

Hi, Can someone please give me some suggestions on how to use a microwave oven to determine the specific heat capacity of tap water? This is not a homework question, but an assignment and I have absolutely no idea how I can do this.This experiment will be done at home, so please no immersion...

Hello; Homework Statement Let \mathcal{A} be the \sigma-algebra on \mathbb{R}^2 that consists of all unions of (possibly empty) collections of vertical lines. Find the completion of \mathcal{A} under the point mass concentrated at (0,0). Homework Equations 1st: Completion is defined as...

hello! I'm investigating on thermal conductivity of concrete blocks. I've got an equation for calculating K, which is Fourier's law. Q'=-k×A× ∆T/l I have to make the experiment simple as possible as i can. My plan is to heat one side of a block of concrete and measure the temperature difference...

This is a old one, but it is rare to find the general solution: Consider a string (a fuse) that, when burned from one extreme, takes one hour to burn, but irregularly (some pieces burn faster than another). Get two strings of this kind. The irregularities are different, you are only granted the...

Homework Statement A chord of a circle subtends an angle of θ radians at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that 4θ = π + 4 sin θ Homework Equations s = rθ area of sector = 1/2 r2θ area of minor...

Homework Statement A particle with charge q and mass m is tied by a (I assumed stiff) string of length L to a pivot point P, all of which lie on a horizontal plane. A uniform electric field E is placed over this system. If the initial position of the particle is at a point where the string is...

All the books I want to read about probability and statistical estimation require some understanding of measure theory. What is a good introductory text on measure theory you would recommend (assuming no prior knowledge of measure theory at all)? I want to be able to teach myself from the book...

I've seen the definition that an outer Lebesgue measure is defined as m_n^* (A) = \inf \left\{ \sum_{k=1}^{\infty} l(I_k) \, \left| \, A \subset \bigcup_{k=1}^{\infty} I_k \right} where Ik are n-dimensional intervals and l(Ik) is the geometric length. It is not actually clear to me if A has...

Hi, We're offered shaving mirrors by suppliers and sometimes their claims to the magnification are doubtful. I don't wish to upset any customers by giving incorrect information. So is there a practical way in which I can test the magnification myself? i.e. measuring the distance of the...

If you have two measurable sets A and B (not necessarily disjoint), is there an easy formula for the measure of the difference, m(A-B)?

I am trying to test different fuel types(for science fair, I am a sophomore in high school) and i was wondering if anyone new something that could be bought or made to measure the force of an explosion. My current ideas don't seem like they would be very accurate. Any help at all would be...

Or how did Coulomb measure quantity of electricity while doing his experiments that leads him to claim his famous Coulomb's law. F=k\frac{q_1 q_2}{r^2} You can measure F and r for sure. But how about q1 and q2 ?

Suppose that E has Lebesque measure 0. Prove that the set {x^2 : x€E} has Lebesque measure 0. Please help me. I have a problem which is unsolveable for me. Thanks!

1. Basically this was a question directed by my subject lecturer. He needs me to describe a method on how to measure the amount of charges stored versus the spacing between the plates of a capacitor. 2. There are many types of ways and equations to measure the amount of charges stored but...

So I was trying to figure out how much power items at my house use. I have a standard looking power meter outside with the dial http://en.wikipedia.org/wiki/File:Electrical_meter.jpg" . I am trying to figure out though what unit the meter uses. My first instinct was watt hour, but I can't get...

Hi, I am pursuing graduate studies in economics, and I hear that "measure theory" is one of the classes that will impress admission commitees. I don't see anything by that name in my school's catalog. Does this class go by another name sometimes?

Dear all, I need a suggestion for my work. I have to measure the variation of some optical features of a material in presence and absence of a magnetic field. Hence, I need to “switch on” the magnetic field in a given instant time, to record the signal an then ““switch off”, or even to change...

Odd question that at first seemed to have an obvious answer: no. It all started when I realized that my friend is horrible at shuffling cards. They fall in large packets such that they fall in layers of unshuffled cards, rather than all of the cards being randomized. Then I realized to...

Some time ago, someone in this forum asked how you measure momentum. One of the answers said that if it's a charged particle, you can let it pass through a bubble chamber and a magnetic field, and measure the curvature of the bubble trail. But this isn't really a direct measurement of the...

I just encountered the Wikipedia page There is no infinite-dimensional Lebesgue measure, and I was left slightly confused by it. They say that a Lebesgue measure m_n on \mathbb{R}^n has the property that each point x\in\mathbb{R}^n has an open environment with non-zero finite measure, and then...

Hi everyone, I'm new to the forum and basically need help to build a little gadget to measure the intensity of light that passes through a tube filled with solutions of different dye concentrations. I have a 10530DAL photodiode, and a light source. What I'm doing now is measuring the...