Measure Definition and 1000 Threads

I read some papers on astrophysics and they discussed dispersion measure. Is there any theoretic meaning of dispersion measure? And what does the unit pc/cm^3 mean?

Homework Statement Let \left\{E_{k}\right\}_{k\in N} be a sequence of measurable subsets of [0,1] satisfying m\left(E_{k}\right)=1. Then m\left(\bigcap^{\infty}_{k=1}E_{k}\right)=1. Homework Equations m denotes the Lebesgue measure. "Measurable" is short for Lebesgue-measurable. The Attempt...

Hi, Homework Statement This is not a formal HW question, yet I was wondering whether one of you might be willing to answer it nevertheless. According to Fraday's law, ε = -∂\phi/∂t. If I reversed the direction of the current in an inductor used to measure ε, would that have any effect on...

I have a final coming up, so I thought I'd post some of my review questions as a way of checking my work. I think I have a working answer for this one, but I'm not sure it's totally right. I'll post it upon request. At any rate, two related questions: (1) Suppose that $$E \subset...

I wasn't quite sure where to put this, so here goes: I am trying to find out some facts about the group SO(2,1). Specifically; Is the exponential map onto? If so, can the Haar measure be written in terms of the Lebesgue integral over a suitable subset of the Lie algebra? What is that subset...

Greetings! Can anyone tell me a little bit about the book Integral, Measure and Derivative: A Unified Approach by Shilov? Is it suitable for self-study? I am wishing to study the basics of measure theory. I will be using the text alongside Kreyszig's Funcational Analysis. Having already...

My understanding is that in general, operators -- corresponding to observables -- act on a state (itself a member of an infinite-dimensional Hilbert space), and the eigenvalue is the value in that state (at least, if it's a pure state). To get an expectation value, you take the dot product of...

I'm trying to measure and regulate gauge pressure in a pipe that has water flowing through it, but I need the pressure to be about .75psi (1.8 ft H2O). Most dial gauge ranges are too high and not accurate enough. Pressure transducers I've had no luck with as far as finding one that's inexpensive...

I have read articles about the GRB measurement using X-ray from afterglow. The article tells that the gamma ray provides poor directional information.Why? How can we use X-ray for measurement?

This is part 2 of a question... I already solved part 1 but I can't seem to be able to solve this one. Interpret the measure √2 μ geometrically? Any ideas... This is from real analysis class Thanks in advance!

I have a non-zero measured subset X\subseteq\mathbb{R}^{n} on which \sum_{i=1}^{n}\psi_{i}x_{i}=0 for all x=(x_{1},\ldots,x_{n}) in X. How can I show that \psi_{i}=0 for i=1,\ldots,n?

Is it the wavelength of the electric portion or magnetic portion or something else entirely?

I am doing a biology project in which I needed to measure the O2 in the test chamber to determine how much activity I had. The Oxygen sensor I bought on eBay was long expired and useless. O2 instruments were at least $120 used. So I began looking for a simple cheap solution to do it with common...

At page 285 in Peskin and Schroeder's Introduction to quantum field theory the author defines the integration measure D\phi = \Pi_i d\phi(x_i) where space-time is being discretised into a square lattice of volume L^4. He proceeds by Fourier-transforming \phi(k_n) = \frac{1}{V} \sum_n e^{-i...

I am trying to understand the measurement of spin, in order to understand Bell's paper on the Einstein-Podolsky-Rosen paradox. When we measure the spin of a fermion in the direction of unit vector a, will the result be: 1. a value of either +0.5 or -0.5, and upon measurement, the fermion...

In quantum mechanics what quantities are actually measured? Measurements of voltage and current are macroscopic measurements of accumulations, right? But when you measure scintillations or spots on a screen that's a point measurement of a particle. I don't suppose you actually measure energy...

How would a strain gage be set up (on top of the model? around the sting?) to measure drag? I don't quite understand the connection between the force of drag and some sort of compression/tension force...? Thanks for the clarification.

This is a simple question. On pages 5-6 of Measure Theory,Vol 1, Vladimir Bogachev he writes that: for E=(A\cap S)\cup (B\cap (X-S)) Now, he writes that: X-E = ((X-A)\cap S) \cup ((X-B)\cap (X-S)) But I don't get this expression, I get another term of ((X-B)\cap (X-A)) i.e, X-E =(...

Hello PF, I am currently studying OLEDs (organic light emitting diodes) and have been reading many articles pertaining to the external quantum efficiency of these devices and the various extraction techniques used. In all of these articles, they state the increase of efficiency but do not...

I'd like to measure the tension and shear forces on several bolted fasteners during a static test. I've looked at these and similar products: http://www.innovationplus.com/index.php ...but it is my understanding that these are only good for clamping force (aka tension force). Anybody...

How can we measure the "reality" in quBits? Hello All matter is based in information, and quantum computing use quBits, so I was wondering how can we measure the reaility in quBits? A certain solid objet, let's imagine an apple, it has a weight and we can calculate (approximately) the number...

Hi, All: I think the following deals with continuity of measure, but I'm not 100%: Let I:=[0,1] , and let An be a sequence of pairwise-disjoint measurable sets whose union is I ( is me? :) ) . Let {Bj} be a sequence of measurable subsets of I , so that, for μ the standard Lebesgue measure...

Due to a homework,i want to measure "ΔBy" component with low orbit satellites,so i can measure Birkeland currents.Does anyone Know how to do it?For example i use the equation J=0.1ΔΒy/Δt.What should magnetometers data measure?Do they measure ΔBy or some other indicator that associates with By?If...

The image attached is of an underdamped RLC step response. I know that I can find the damped frequency of the response by first finding the period of the wave, and manipulating the period such that I can do 2*pi*f. If I'm looking at this waveform and the only info I know about it is this...

Hey Folks Quick disclaimer: I have no background in physics whatsoever but I have found myself trying to solve a problem that is seemingly based in physics so I am trying to learn. I also have a background in search and search engine optimisation which usually means I am a dab hand at...

Unfortunately when I google the answer, the results are just how to use a balloon to measure air pressure. I want to be able to monitor the internal pressure of a balloon using a digital barometer. 1) How would I go about setting up such a system? 2) Would the barometer have to be on the...

Hi members of the forum, Problem: In triangle ABC, D is the midpoint of AB and E is the point of trisection of BC nearer to C. Given that $\displaystyle \angle ADC=\angle BAE$, find $\displaystyle\angle BAC$. I have tried to solve it using only one approach, that is by assigning...

I take a rod and attach to its ends a another rod parallely at a distance r. The second rod oscillates about the first one through 180 degrees with some time period 't'. Now I am in a frame in which this system is moving at a speed 'v' with respect to me. I keep some sand in the way of this...

As we know EM waves have a wave length. Well, how do you measure them? I have the feeling there is a path from point A to point B and that path goes up and down at a regular rate and all photons travel along that wave-path and that they are no where else between A and B but on that path. But...

I was reading a little about measure theory, and the measure of a singleton is zero. So why couldn't we just describe the reals as an uncountable number of singletons which each have zero measure and then union all of these singletons. Maybe the union only works for countable sets when...

Does it also imply that the set is dense?

Hello, I'm working on a design for an architectural structure, and I am choosing the material for the design. Are there any resources that will tell me the breaking point for like "1-inch" of material X. I need something that can support the weight of a car. Thanks! Carpetfizz

Good Morning, I was using the Digital Multimemter (DMM) a couple days ago and was wondering what inside the DMM (Circuitry) enables it to measure the current running through my circuit. I thought that it was a resistor with a preset resistance where the DMM measures the voltage potential...

Homework Statement Let E have finite outer measure. Show that if E is not measurable, then there is an open set O containing E that has finite measure and for which m*(O~E) > m*(O) - m*(E) Homework Equations The Attempt at a Solution This is what I did... m^*(O) = m^*((O \cap E^c) \cup...

I have 2 questions about the attachments. 1) In the second attachment, I'm a bit confused about the thing that I marked: O \sim E = \cup^{\infty}_{k=1} O_k \sim E \subseteq \cup^{\infty}_{k=1} [O_k \sim E_k]. I just don't understand how \cup^{\infty}_{k=1} O_k \sim E can be smaller than...

Homework Statement I am doing a lab and need to understand how laser light from a HeNe laser goes into a Si photodiode connected to a lock in amplifier, which I believe is simply a device for measuring potential, works. Homework Equations The Attempt at a Solution This lab was...

I have not yet studied experimental physics!But I would like to know how can we measure the mass of quark,because we can not to have separate quark for color confinement.In quarkonium,by resonance we know the excited state of quarkonium,but how can we know which state they lie(e.g 2^{3}S).

Gauss equations state that the flux of a gaussian surface is equal to the sum of all the electric field times the surface area. Although he stated this in theory, how was he able to prove it possible. What measuring device do people use to prove that this theory is correct?

Can anyone share a review of this book with me? I am thinking about purchasing it, and I would like some feedback. Please note that it will be used for a self-study. Thank you.

I am trying to prove if f and g are Riemann integrable, then fg is also Riemann integrable using Lebesgue's integrability criterion. I already proved that a Riemann integrable function is bounded. Not much harder to show fg is too bounded. How do I show that [a,b] is of measure zero? I can't...

For a 2D vector field {F}=P(x,y)\vec{i}+Q(x,y)\vec{j} curl {F} = \frac{\partial Q}{\partial x}+\frac{\partial P}{\partial y}\vec{k} So that's the rate of change of the j component of a field vector with respect to x plus the rate of change of the i component with respect to y...how does...

Do you think having Bogachev's Measure Theory (vol. I) as a first exposure to measure theory sounds a good idea? I mean while I can understand well the concepts presented in the book, I find some techniques used in the proof section quite hard to follow. :confused:

Could we use the fact that all countable sets have zero measure to prove that their must be a larger infinity. we know countable sets have measure zero because I could just start by making boxes around each number and then add up their widths. For the first number I will make a box...

Entropy is a measure of energy availiable for work ? "Entropy is a measure of energy availiable for work". Can someone explain this to me? Give some examples that show in what sense it is true. It has to come with a lot of caveats, proviso's etc. because its simply not true on its face. I...

I know the textbooks say light travels 186,282.4 mps, but if time slows for a very fast object, how do scientists really know the speed of a photon?

Homework Statement Prove (using Lebesgue outer measure) that $$m_{2}^{*}(\{(x,y)\in\mathbb{R}^{2}\colon x>1,0<y<x^{-2}\})=m_{2}^{*}(A)<\infty$$ The Attempt at a Solution I'm not sure if this is valid proof but I'd have done it like this: $$\int_{1}^{k}\left|x^{-2}\right|\, dx <\infty \forall...

[SOLVED] how to build a device to measure in angstroms Hello, I was looking at a micrometer and wondered how one could build a similar device for meauring in angstroms. Could someone point to some theory that discusses the same ( for example if i have to forge a screw what would be its...

What is a measure of "jointness" of a joint distribution? Correlation?

Hello, I have a particular derivation of a four-vector integration measure, basically changing the measure to some related more useful measure - but I'd like to do this in 3-vector notation. Here it is, from the integral...

A friend asks me this. If considering the equation: ∫\frac{dQ}{T}, then it is technically feasible to work out some forms of expressions with measurable physical quantities like temperature and specific heat, therefore it is possible to work out a precise value for entropy change. But is there a...