Measure Definition and 1000 Threads

how to measure perimeter without pi? [before they knew about the pi ratio]

Note: I have never formally studied number theory so what I'm about to ask may be either completely trivial or completely meaningless. In either case, I don't know what to search for to find my answer since I don't know the terminology. Is there a measure of how far from a prime a given...

I am a bit confused about what accelerometers actually measure and hopefully somebody can help me resolve the following scenario: Say we have a vehicle with mass m, fixed CG location and subject to gravity. The vehicle is traveling at constant speed in the X direction heading to a cliff...

Homework Statement http://meinprojekt.hostzi.com/images/Picture2.jpg We did an experiment to measure E mf or the cell voltage of bateries. A thin wire (slide-wire potentiometer) is connected into the circuit. From point a to c the resistance along the wire is 36 Ohm. Depending on where the...

Suppose that antiferromagnetic material have two sublattice. How can we measure magnetisation in sublattice A and in sublattice B? Maybe neutron scattering? How that work? Is NMR good solution maybe?

Can we really measure a physical property of something, without changing it in any way at all? In a circuit, you cannot use a voltmeter to measure a voltage without changing the circuit. The change may be small or negligible in most cases, but it is there. If you use a thermometer to measure...

Thought experiment. Let's imagine I'm on my spaceship moving in the void. For this example, I'm assuming my flight started on the Earth, where I could see the ground and landscape and thus I was able to tell that I was moving; however, without accelerating or decelerating, I progressively got...

Homework Statement I am trying to prove that if f is continuous almost everywhere on [a,b], and if g is cont a.e. on [c,d], with f[a,b] contained in [c,d], then g composite f is cont. a.e. The Attempt at a Solution ------ Originally, my proof went something like this: f is cont...

Homework Statement Let \mathcal{A} be σ-algebra over a set X, and μ a measure in \mathcal{A}. Let A_{n} \in \mathcal{A} with \sum_{n=1}^{\inf} \mu(A_{n})< \inf Show that this implies μ ({x \in X : x \in A_n for infinitely many n}) = 0 . The Attempt at a Solution I don't even see how is the...

hi, i am learing about measure theory and i am looking fore some good reference of the subjects ..

I'm going in circles on units (or perhaps more accurately different unit systems). The two my professor has chosen to work in are Gaussian units and MKSA units. My problem is one of lack of understanding; are the units of measure for electric and magnetic fields in these systems: Gaussian: E...

A few shopping centres in my area have these devices that can measure your weight and height. I figured I'd try it out, all you had to do was insert a $1 coin. Thing is, it has this type of tube on the top of it (the actual device was in an elongated C shape with a small platform to stand...

[b]1. x^-2dxdy and x^-1dxdy are left haar measure and right haar measure respectively how?

I saw this problem on this site a while back and started to think about it. I can't find the post so I'll start it anew. The problem is: can you have two disjoint sets dense on an interval so that the measure of each set on any interval of that interval is equal? That is, say you have A, B in...

We learned yesterday that a voltmeter's resistance approaches infinity. And that infinite resistance means total disconnect. I'm trying to understand why is that? Why must a voltmeter's resistance approach infinity? Doesn't it mean that the voltage will be 0? BTW - I hope I'm translating...

Dear Friends & Colleagues, I would like to propose the following Question, Is there a way to technically Measure the Gravitational Pull of a body? (body being any of the following: molecule, physical item like a rock, or a planet or a star). I am not looking for a sample of a falling...

Hi, everyone. I would to identify colors (fur colors, in this case, but I suppose that's not important) with greater precision that using color words, (eg. Rufus). Ideally, I'd use a spectrometer to find reflectance curves, but I don't have one, so I thought that using a digital camera...

The double slit experiment is often described like this: (I'll describe the photon version, but of course the electron one is the same) "We fire individual photons at a screen with two slits. An interference pattern appears. But when we try to look at the slits to figure out which slit the...

Supposedly, you use a certain type of seismometer. But in that case, how could a deep earthquake far away register as "higher" than a shallow earthquake that's up close? Sure, the deep earthquake may release more energy, but much of it is dissipated by the time it reaches the seismometer (and...

We have a customer asking us for the thermal conductivity of a product we sell. None of the engineers have that number. I can think of a simple experiment that might do it, but I don't know the math. I want to take a piece of this material (it's a pipe), put a cap on the bottom, then...

Homework Statement Suppose f\in L^2[0,1] and \int_0^1f(x)x^n=0 for every n=0,1,2... Show that f = 0 almost everywhere. Homework Equations My friend hinted that he used the fact that continuous functions are dense in L^2[0,1], but I'm still stuck. The Attempt at a Solution I need...

Homework Statement Let A be the set of all rational numbers between 0 and 1. Show that for any "finite" collection of intervals I_n that cover A the following inequality holds: \sum I_n \geq 1 . Homework Equations We are using the definition of the outer measure here. Where the outer...

Homework Statement \mathcal{A} is a \sigma-algebra, A_n,A\in\mathcal{A}. Prove that if A_n\uparrow A in \mathcal{A} (i.e., A_1\subseteq A_2 \subseteq ... and \bigcup_{n=1}^\infty A_n = A), then \mu (A_n) \uparrow \mu (A)The Attempt at a Solution The up-arrow notation is defined on these sets...

I got to measure the diameter of a marble with a micrometer. Whatever the diameter and the radius be, it doesn't matter here and calculate the volume of the marble I was told to use the formula " V = Square root of (4/3 * 22.7 * rcube)". Then the last question was asked: "Give 1 practical...

For my Advanced Higher Physics Investigation i am measuring acceleration due to gravity. Having already done it with a simple pendulum my teacher says i have to do the same with a "Compound Pendulum". I was wondering how to do this and also how to make a compound pendulum with a steel rod...

let f_n be series of borel functions. Explain why set B = {x: \sum_n f_n(x) is not convergent} is borel set. Proof, that if\int_R |F_n|dY \leq 1/n^2 for every n then Y(B) = 0.Y is lebesgue measure.for first part i thought that set of A={x: convergent} is borel, and B=X\A so it's also borel...

A set E subset of real numbers has measure zero. Set A={x2 : x\inE}. How to prove that set A has measure zero? (E could be any unbounded subset of R)

Homework Statement The question is from Stein, "Analysis 2", Chapter 1, Problem 5: Suppose E is measurable with m(E) < ∞, and E = E1 ∪ E2, E1 ∩ E2 = ∅. Prove: a) If m(E) = m∗(E1) + m∗(E2), then E1 and E2 are measurable. b) In particular, if E ⊂ Q, where Q is a finite cube, then...

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...