Measure Definition and 1000 Threads

Hello all, I am looking for some guidance on making a mechanism that will retract a 900 metre length of fishing wire by itself. The idea is that the wire can be pulled up to 900 metres from its source and once let go it will return to the spool like a tape measure (without a crank or...

This question came up recently, and I'm wondering whether or not it's true: Let (X,A,m) be a finite measure space. Let E_1,E_2,... be a sequence of measurable subsets of X of constant positive measure (i.e., there exists c>0 such that m(E_i) = c for all i). Then there exists a subsequence of...

I was wondering, are mass and energy specific to a particular reference frame, as well as things like time? Let's say for example, there's two observers, one in motion (A) and another stationary (B) standing along side my path of direction. If I were in accelerated motion, observer B would...

In the UK we live in a society which insists that all that matters is education and economic output, while the value of 'true love', which comes to us all in our teens, is widely denied. As a result, we are left with a 'broken' society, where 50% of relationships fail and where personal greed...

What theory are they? Set theory comes to mind but is that too broad?

Homework Statement Let (X_n) be a sequence of measurable subsets of \mathbb R such that \sum_{i=1}^\infty m(X_i) < \infty Define X = \bigcap_{i=1}^\infty \left( \bigcup_{j=i}^\infty X_j \right) Prove that m(X) = 0. Homework Equations Theorem. Let (E_n) be a sequence of...

Ok, here's the deal. I am trying to measure how much energy (best in watts, i guess?) a device uses over a seven hour period. I bought a device from lowes that measures watts and amps but how do I figure out [for example] if it says a device is using 8 watts and .2 amps right now, how much...

Homework Statement Let D be a class of sets of space X. There exists a unique smallest ring, R, containing D The Attempt at a Solution I'm working on the existence part. If D were finite, I think that it would be possible to use set differences to find a set, D', of smaller sets...

Hi: I am trying to review the way L^p spaces are treated differently in Royden. In Ch.6, he treats them under "Classical Banach Spaces", and then again, in his Ch.11 , under "Abstract Spaces". This is what I understand: (Please comment/correct) In the case of abstract...

What does it mean by \int f(w) P (dw) I don't really understand P (dw) here. Does it mean P (x: x \in B(x, \delta)) for infinitely small \delta ? For example, with P(x)=1/10 for x=1, 2, ..., 10 . How can we interpret this in term of the above integral Thanks...

1. Is an annual increase of lightning strikes worldwide a measure of global warming? 2. What has been the correlation between such discharges and temperature in recent decades?

Just for fun, I was thinking of trying to design one. How could we design a thermometer that could accurately measure negative temperature of a spin system?

My homework problem says to construct a thermometer which could accurately measure a negative temperature. I have no idea how to do this. Any help would be very appreciated!

Homework Statement Construct a sequence (G_n) of dense open subsets of \mathbb{R} such that \lambda \left( \bigcap_{n=1}^\infty G_n \right) = 0 and hence deduce that there exists an uncountable subset of \mathbb{R} of measure 0 Homework Equations \lambda is the Lebesgue...

Homework Statement An accelerometer—a device to measure acceleration—can be as simple as a small pendulum hanging in the cockpit. Suppose you are flying a small plane in a straight, horizontal line and your accelerometer hangs 12° behind the vertical, as shown in the figure. What is the...

Homework Statement To measure the acceleration due to gravity on a distant planet, an astronut hangs a 0.055 kg ball from the end of a wire. the wire has a length of 0.95 n and a linear density of 1.2*10 ^-14 kg/m. using electronic equipment, the astronaut measures the time for a transverse...

http://webusers.ct.astro.it/gca/papers/telluric.pdf Would it be possible to use telluric lines to give accurate measurements of atmospheric gases along with synchronous Earth temperature measurements, thus giving an index for gas abundance and variation of heat transfer through same gases...

anyone know how scientists measure the rotation period of the moon? thank you!

Hello, I would like to know different ways to measure the speed of light. It's for one of my project. I would like to know if there are simple ways to do it. I already know that we can measure the speed of light using a microwave...

Hello, folks. Q: How can one measure the density of states of a semiconductor and a conductor? I would imagine you want to measure the charge carrier density and then you can calculate the density of states. If so, what observable(s) can yield the charge carrier density? How can you...

suppose I have a long thin pipe. There is some liquid inside (probably water, but can add stuff to it if needed). On a certain segment of the pipe I want to measure the velocity and/or pressure of the liquid at various points along its length and feed the results into the computer. Flow of...

Thanks a lot for everybody's answers. Upon some consultation with others I have concluded that this just seems to be the wrong way to solve what I am trying to solve. Sorry about this. ----------------- suppose I have a long thin pipe. There is some liquid inside (probably water, but can add...

Homework Statement A Doppler blood flow unit emits ultrasound at 5.0 {\rm MHz}. What is the frequency shift of the ultrasound reflected from blood moving in an artery at a speed of 0.20 m/s? What equations would I use to calculate the doppler shift? It is not in my textbook...

Is this true? V\subset\mathbb{R}^n\;\textrm{open}\quad\implies\quad m_n(\partial V)=0

What is the definition of a fat cantor set? How do I show that the fat cantor set has positive Lebesgue measure and does not contain any interval. I know for the cantor set that at each stage, we remove the middle third of each interval starting with [0,1]. I am wondering if instead for the...

I'm doing some experiments, and I need to measure the current (and/or voltage) going through several loops of wire as a magnet slides through. The magnet slides parallel under the loops at a certain speed. I have a multimeter and an ammeter. The problem with the ammeter is that it's just a...

I have a cylindrical neodymium magnet. I know that the magnetic field varies with distance, but how would I determine the magnetic field B at a certain point, through experimentation? I know how to find the force between two magnets at different distances by balancing out with gravity, but I'm...

This is actually a question extracted from the physics book by Halliday. How would you suggest measuring the temperature of (a) the Sun, (b) the Earth's upper atmosphere, (c) an insect, (d) the Moon, (e) the ocean floor and (f) liquid Helium? Thanks first.:smile:

Homework Statement (X,S,u) a measure space and f is in L1. Show that for any e>0, there exists a set E with u(E)<+infinity such that | \int_{E} fdu - \int_{X} fdu |<e The Attempt at a Solution we can define a function v(A)=\int_{A}fdu It is a well known result that v(A) is in fact...

I need please ideas how to use DAC to measure current.Currently I have built DAC to measure voltage, the type i built is the STAIRSTEP RAMP the 8 bit one.

Homework Statement In the measure space {X,S,u} where u is the counting measure X=(1,2,3,..} S= all subsets of X fn(x)=\chi{1,2,,,..n}(x) where \chi is the characteristic (indicator) function. Does fn(x) converge a.pointwise b.almost uniformly c.in measure Homework Equations...

What is the device used to measure percent light absorption in pigments? I remember finding the percent light absorption in the pigments of some vegetables for a high school bio lab. I am pretty sure the device used was not specific for pigments. The device was user friendly- we just stuck...

I need some guidance into understanding Radian Measure and the Unit Circle. This was the topic where I tanked and had to drop the course. I'm going to pick it up again next fall and want to start preparing now. Any help is appreciated. Sean

Hi there, I just wonder how to measure the square of angular momentum and the z componet of angular momentum in QM system? If I have two spin (marked as 1 and 2), why J^2 (total) doesn't commute with J_{1z} or J_{2z} ? or why they cannot be measured at the same time? (Well if I calculate the...

The multimeter in our lab has temperature measurement function. I am wondering how it works. Can it measure temperature of insulating materials or it just work for metal?

Can anyone tell me if there's a device or method to DIRECTLY mesaure the frequency of a light source? Thanks, Joe M.

Homework Statement A wave source approaches you at constant speed and you measure a wave frequency f1. As the source passes and then recedes, you measure frequency f2. Find the expression for the frequency emitted if the source were stationary in terms of f1, f2, and wave speed v...

Hi, Im investigating how infra red is affected in different areas e.g at home, out side, in the dark or in light. To do this i have made a circuit with a photodiode from the company rapid. The problem is that the photodiode is operating as just a switch, saying if the infrared is on or off so i...

Short version: What is the difference between the Lebesgue measure and the box counting dimension of a set? Long version: I was reading up on the definition of the Lebesgue measure, and the description of how to take the Lebesgue measure of a set (which I understood basically as "cover the...

If a sequence of measurable functions (real-valued) converges in measure, is it true that you can find a subsequence that converges almost uniformly? (This is obviously true if m*(domain) is finite...but in general is it?) If so, can someone outline a little why?

Alright I have to questions one is on how to measure the time it takes for my computer to solve a particular code I've tried the the "tic toc" and that seems to be dependent on the time frame that I typed in tic and toc. I need something that Is only dependent on the time taken to process and...

I was told that you can find a disjoint sequence of sets...say {Ei} such that m*(U Ei) < Σ m*(Ei).. That is the measure of the union of all these sets is less than the sum of the individual measure of each set... This is obvious if the sets aren't disjoint...But can someone give me an example...

Im doing a school project where we need to come up with an accurate way to measure the moons orbital velocity with an experiment... My plan was to find the radius of the moons orbit, then its period, and based on a distance over time find its velocity. However i realize I am making a serious...

What position should you start to time the period and why? Should you start to time the period straight away or wait, and if so for how long (how many oscillations)? If the length is fixed should you use a long or short pendulum to increase precision? If the mass is fixed should you use a large...

Is there a way to have some observables, apply an equation and find a measure if the system is chaotic or not? For example, measure the time-dependent displacement of the wings of an airplane, apply some analysis and then say "OMG! And I mean O.M.G.! We are in the chaotic regime. Better do...

On General Measure of Entanglement Hi, sirs My major is computer science. While I currently need to deal with some physical problems. Thank you very much for your help. It is well-known that Von Neumann entropy is a measure of entanglement for bipartite pure states. However, I...

Hi, guys! I am a high school senior, I would like to ask you a few questions about how to measure the released energy during physics experiments, especially both nuclear reactions. Also, how could Fermi just know the "yield" just by a handful of torn paper? Thanks for your reading!

Hello all, In order to re-use formaldehyde from a dilluted solution (in water) I need to know the concentration of formaldehyde in the dilluted solution. Can anyone tell me how to measure this concentration? It does not have to be very accurate. thanks in advance, Albert

Hi all, i have been assigned to study indoor air quality and car cabin air quality project. My Problem is: How to measure Carbon Dioxide concentration in that constant volume of air? (consider there will be changes in the concentration and i need to quantify or contrast it at least.)...