Measure Definition and 1000 Threads

Considering they will eventually be colliding gold or lead ions, will they measure or be able to measure the gravitational impact of the collisions? Just curious since the velocity will be so extreme. I would think Tevatron would already have something to say about this, but I'm unsure of...

Hi All, I am a new phd student in engineering, working in signals analysis in neuroscience who seems to be doing a lot of work in statistics and probability theory. My uni is offering a course in measure theory. The course profile says: "The course is an introduction to measure theory and...

Homework Statement Given a measure space (\mathbb{R}, \mathcal{B}(\mathbb{R}),\mu) define a function F_\mu : \mathbb{R} \to \mathbb{R} by F_\mu(x) := \mu( (-\infty,x] ). Prove that F_\mu is non-decreasing, right-continuous and satisfies \displaystyle \lim_{x \to -\infty} F_\mu(x) = 0. (Right...

Homework Statement Let (X,\mathcal{A},\mu) be a fixed measure space. Let A_k \in \mathcal{A} such that \displaystyle \sum^\infty_{k=1} \mu(A_k) < \infty. Prove that \begin{align*} \{ x \in X | x \in A_k \text{ for infinitely many k} \} \end{align*} is a null set. Homework Equations The...

I just finished a course where we discussed concepts such as Lebesgue integration and Lebesgue measure of sets. Today, I was telling my brother about how the irrationals on the interval [0,1] have measure 1, which is sort of counter-intuitive. Anyway, he proposed the following question. Let A...

It's a really tricky one to work out, but does anyone have any suggestions of how to measure compressive strength? Thanks a lot.

Hi In my shop, i have to design a fixture & want to calculate the force exerted by a moving element. Can anyone let me know the simpliest formula to calculate force ? Zirok

This is a practice final exam problem that has been giving me fits: Let E be a Lebesgue measurable subset of the interval [0,1] that has finite measure. Show that there exist two points x,y \in E such that x-y is rational.

I have teenaged daughters, and like many of their peers, they're obsessed with their body weight. Unfortunately, since I have access to accurate scales at my gym, I've never bothered buying a bathroom scale at home, and this is now becoming a source of friction. Rather than simply surrender...

Homework Statement Suppose that if k is a measurable function and {x : k(x) > 0} has a positive measure, then {x : k(x) >= p} has positive measure for some p > 0 Homework Equations Lebesgue measureThe Attempt at a Solution What is positive measure? is it just another word for measurable? Can I...

I would like to measure the distance between team players in the field. I need a device that can signalize when a distance between 2 players of the same team approaching a certain distance (2, 3 or 4 meters). The device must be relatively small (in order to have in on a players), to...

Dear all: I want to make a chamber as O2-free. The chamber is not perfectly sealed, so it has some small holes. I have used N2 gas (by pumping N2 from one input and escaping of O2 from holes in junctions). Now, I want to measure the amount of remaining O2 inside chamber. How can I do that? Is...

hi, i measured the emission spectrum of an LED with a monochromator connected to a PMT tube. the spectrum was measured at four different gain levels on the PMT. i want to check the PMT's linearity at the different gain level, so i want to compare the four data sets and check their...

Why is the measure and "finititude" of c critical? Why is it that c plays such a huge role in SR? Is it the actual relative measured speed of c, or is it that it's finite or both? I know that this may seem mirky. I "get" time dialation, length contraction, dopppler shift... What is the...

How can you measure the mean density of a neutron star if your only told its mass is three times that of the Sun?

I'm trying to measure solar radiation. Unfortunately I currently live in Bolivia, so I cannot get a solar cell. Instead I wanted to use a photodiode, but I wasn't able to find that either. Do you think that it is possible to measure solar radiation using a LDR? What about a phototransistor...

All I know is that polarization density satisfies two equations \[ \begin{array}{l} \rho _{bound} = - \nabla \cdot \vec P \\ \sigma _{bound} = \vec n_{out} \cdot \vec P \\ \end{array} \] This is the divergence and boundary conditions of P.But to determine a vector field...

I just beginning to study measure theory. so far from what i understand so far , can we say in general, an integral is a measure, (ie it is nothing but a set function. a mapping F : \mathcal{F} \rightarrow \mathbb{R} where \mathcal{F} is a family of sets. does it make sense to say in...

Today my sister asked me to measure her height so she can calculate her BMI. Being the lazy lout that I am I told her to measure herself. And then I started thinking of ways she could actually measure herself. I am embarassed to admit I could only think of two ways: 1) Let's round out her...

I need to measure the capacitance of something as accurately and as quickly as possible. I also need the method to be very noise tolerant and not depend upon signal attenuation. I've been looking at several different methods so far on how to do this and so far I have found methods like the UTI...

I'm tinkering with a simple heat engine and I want to experimentally measure its work output. The engine pushes a piston once per test, and I know the work done is on the order of 1 kilojoule. The problem is that the engine does the work on the order of milliseconds, but depending on the...

i want to use measure the frequency of the square wave input at RA4/T0CKI of PIC16F84. so how should i start writing the code? anyone can provide some draft of the c code? thanks.

HI, THIS IS MY FIRST POST. I AM ACTUALLY A STUDENT AT A UK COLLEGE AND I AM STUDYING ELECTRONICS. I HAVE ALREADY PASSED MY COURSE WITH FLYING COLOURS WITHOUT SITTING MY FINAL. I AM NOW WORKING ON A PERSONAL PROJECT AT HOME. IM JUST HOPING THAT SOME OF YOU GUYS COULD LOOK AT THYE ABOVE CIRCUIT...

Homework Statement Show that if E \subset B and B \in L(\mathbb{R}) (where L(R) denotes the family of Lebesgue measurable sets on the reals) with m(B) < \inf , then E \in L(\mathbb{R}) if and only if m(B) = m^{*}(E) + m^{*}(B - E), where m^* denotes the Lebesgue outer measure.Homework Equations...

1. Suppose you are on the bank of a river at night. Opposite you on the other bank is a street light. You have a sensitive light meter and a meter stick. How wold you determine the distance across the river?

Hi I'm interested in measuring the recoil force of a weapon. Anyone got any ideas om how to go about doing this? I was thinking of using a load cell mounted to the weapon in the horizontal plane, but at the same time the weapon needs to operate more or less freely, which will be difficult...

I am trying to learn about Lebesgue measure. One of the questions I couldn't solve is this; Show that the following sets are Lebesgue measurable and determine their measure A = {x in [0,1) : the nth digit in the decimal expansion is equal to 7} B = {x in [0,1) : all but finitely many...

how to measure water level in a tank?? How to measure water level in tank in the cheapest way? The first thing that came to my mind is pressure sensor... but it's ruled out because it's expensive. Can somebody suggest a cheaper mechanism? And it is preferred to have a low power mechanism...

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...

I got in a global warming topic and some people are saying that historical temperature records are inaccurate. So I'm wondering if there are any reliable ways to measure historical temperature.

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...