Measure Definition and 1000 Threads

What might be the best way to measure speed and location of a car that move's toward me

Homework Statement I have a sequence of functions converging pointwise a.e. on a finite measure space, \int_X |f_n|^p \leq M (1 < p \leq \infty for all n. I need to conclude that f \in L^p and f_n \rightarrow f in L^t for all 1 \leq t < p. Homework Equations The Attempt at a Solution...

Hello, I'm not an electrical engineering student so please bare with me... anyways if let's say you swallow a pill containing a piezoelectric sensor to measure adsorption of a molecule in the stomach how can you detect the changes in frequency? if there is no "physical" electrical connections...

How do you measure the voltage of a cockcroft walton multiplier over time to observe the charging behavior? Does measuring with oscilloscopes discharge the capacitor hence you can't observe the charging or not?

Wgat would a "light clock" measure in free fall? I've read in a couple of different books that the similarities between acceleration from gravity and rockets or whatever is only local. Both books said one of the reasons is because with acceleration from gravity two objects in free fall starting...

The canonical example of a function that is not Riemann integrable is the function f: [0,1] to R, such that f(x)=1 if x is rational and f(x)=0 if x is irrational ( i know some texts put this the other way around, but bear with me because i can reference at least one text that does not). Hence...

So, first off, I'm thinking Lorentz invariant quantities are the same in any inertial frames S and S' regardless of their relative velocity. I'm thinking I need to show that \frac{d^3k}{(2\pi)^32E(\vec{k})} = \frac{d^3k'}{(2\pi)^32E'(\vec{k'})} where the primed & unprimed quantities denote...

Homework Statement While studying a book "analysis on manifolds" by munkres, I see a definition of measure zero. That is, Let A be a subset of R^{n}. We say A has measure zero in R^{n} if for every ε>0, there is a covering Q_{1},Q_{2},... of A by countably many rectangles...

Someone tells me that every objects has its own vibration, such as stone, water ... When bee is flying, the sound of vibration can be heard at different speed, bbbbbbb ... but not all vibration can be heard by us. Does anyone have any suggestions on what kinds of device can measure...

Homework Statement Prove that if f: [a,b] -> R is absolutely continuous, and E ∁ [a,b] has measure zero, then f(E) has measure zero. Homework Equations A function f: [a,b] -> R is absolutely continuous if for every ε > 0 there is an δ > 0 such that for every finite sequence {(xj,xj')}...

Hi, I have 2 coils arranged next to each other. One of them is used to generate alternating magnetic field at several Hz, and the other one also generate alternating magnetic field but at higher frequency (several kHz). Are there any magnetic sensors that can measure only the...

Hi guys, I had been wondering for a while why it is that we use the radian as the unit of angular measurement in higher sciences and mathematics (calculus, physics, engineering) as opposed to the degree. In reviewing the relationship between the degree and radian, I believe that I have...

Homework Statement Two girls are arguing about which is able to hit a hockey ball harder. Describe an experiment which they could carry out to measure the average force between the stick and ball during time of contact. Homework Equations Force * Time=Change in Momemtum (Mv-Mu) The...

Hi, i wanted to know how you measure the squishiness of something, like a small piece of rubber. Is there some sort of tool that does this?

Homework Statement Hi, I have been given a coursework assignment to devise a means of measuring acceleration of a space capsule, to measure acceleration during space travel. This must be attached to an appropriate place in the capsule. My lecturer hinted that this could be done by...

can you simply extract the elasticity from ultrasound medical images? I don't know ultrasound very much but I just found out it can measure elasticity. under what condition can ultrasound be used to measure elasticity of some deformable object and do ultrasound medical images qualified for...

Homework Statement Let f:[a,b] -> R be a bounded function, and let D be the set of points at which f is not continuous. (a) Prove that D is a countable union of closed sets. (b) Prove that if m(D) = 0, then f is measurable. Homework Equations Of(x) = lim(ε->0)(sup f(y) - inf...

What do we meen by "Normalize Lebesgue Measure", when we talk about functions on the unit circle. If some example is introduced it will be better (how to evalutae the integral).

set up 12v bat. to 150w inverter to a tower pc. so i put a amp meter between 12v bat and inverter .times the volts by amps get wattage? then get the wattage of computer using a mains socket(because the inverter produces modified sinewave and my wattage meter may not work...

"Except on a set of measure epsilon" vs "Almost Everywhere" There are certain results in analysis which say that a property P holds everywhere except on a set of arbitrarily small measure. In other words, for any epsilon you can find a set F of measure less than epsilon such that P holds...

To start with, I have never been in a physics class, nor am I an engineer. I am a computer programmer, and I love the science channel, so at best I am a bad amateur in this field of study. That being said... I was thinking about calculations that could be used in games like Angry Birds, and I...

Hi, i hope someone can kindly give me some opinions for my idea :) I've a project related to vortex induced vibration. The prototype has a cylinder submerging into moving fluid, and it generates a upward/ downward motion in cycles. I want to measure the efficiency of my prototype, which...

Is it true in general that if f is Lebesgue integrable in a measure space (X,\mathcal M,\mu) with \mu a positive measure, \mu(X) = 1, and E \in \mathcal M satisfies \mu(E) = 0, then \int_E f d\mu = 0 This is one of those things I "knew" to be true yesterday, and the day before, and the...

To start, I'm not at all knowledgeable in physics; completely ignorant. Now, I know I could go ahead and research this on my own, but I've always felt like asking an actual interactive human being is the best way to gain direction compared to a lifeless search engine or book. So how do we know...

I have understand that the Parallax method can be used to measure the distance to stars, but what happens when the parallax angle gets to small to be measures accurate? What kind of methods are used to measure distance to star that are like 5000 light years away, or to Superclusters that are...

for one section of my project, i need to know the phase difference between two signal. they are both 40MHz, but out of phase by a certain angle. i have a AD8333 board from Analog Devices, it is a dual I/Q demodulator consist of double-balanced gilbert cell mixers. The board has 2 RF inputs, a...

People take the liberty in using statements like "choose an integer at random," usually meaning consider the integers to be equally likely. Show that this statement is truly void of meaning by demonstating that there does not exist a problability measure that addigns equal problability to all...

Hi. I have a proof of a very basic measure theory theorem related to the definition of a measure, and would like to ask posters if the proof is wrong. Theorem: If E is measurable, then \overline{E} is measurable and conversely. My Proof: Let's try the converse version first. m(E)=m(E \cap...

i have a project where I need to measure 2 different angles and then take those 2 measurements and compute a final number. I was thinking about using inclinometers to do the measuring of the angles but am really stuck on what hardware/software to use. I was hoping to find something that is...

Hi folks :smile: I have an experiment in which I take an image of a flame. I then run a software routine that tells me what the concentrations of OH (hydroxyl) is at different heights above the flame. I first have to give it a calibrated image of a flame with known data and it then is able...

I have a plastic disk 0.5" in diameter whose radius of refraction is supposedly non-uniform. It will vary by 0.015 at most from the center to the outside. I need to come up with some method of measuring the refractive index locally. I have access to: helium neon laser a photodetector and...

power is the measure of rate of change of energy in any circuit,then how the energy is changing in any circuit or how the change in energy happens in circuit? thanks.

I'm trying to find a certain type of scale that will measure the pressure I exert on it but I'm not really an expert on scales. I need one that will easily read the amount of pressure when I'm grabbing a counter or something and pulling my body weight down upon it. So I need one that can measure...

hi i want to find the output impedance of the following cct so i can perform pi matching on it but i don't know how to find it using lt spice please help! added schematic

Dear all, I am trying to understand something for SNR, I know that is the ratio of the Power of a signal divided by the Power of noise. According to wikipedia Signal-to-noise ratio is defined as the power ratio between a signal (meaningful information) and the background noise...

For this lab, I'm supposed to use materials that heat up but doesn't allow heat to transfer. I've used raw spaghetti noodles already but I still a few more for more trials. So what materials are good for this lab? after heating up the material, I measure the distance between the "hot spots" so...

Ok, so given two hypothetically identical systems (like two spaceships with identical mass, onboard matter, etc.) am I correct in thinking that if the two to accelerate to different speeds and fall back to the same speed, the one that was traveling faster will have experienced a lesser degree...

Homework Statement Suppose you know the wavelength of light passing through a Michelson interferometer with high accuracy. Describe how you could use the interferometer to measure the length of a small piece of material. 2. The attempt at a solution - Sandwich the piece of material behind...

Guys, I'm taking real analysis starting with open, close, compact sets, and neighborhoods. Now I'm addict to rely on these concepts to do my proofs. In the future I will have to take Measure Theory. Can anyone give me a percentage indication for how many percent theorems are proven by the set...

How could one measure degree of coherence with Fresnel biprism? Hello. I have some questions about the study of partial coherence with a Fresnel biprism. In common text degree of coherence and its relationship to visibility is introduced considering a Young Double Slit experiment. At the...

Can you give example of systems that self collapse? For example, is radioactive decay an example of self measurement? How about 13 billion years ago when stars were just being formed, is it an example of self measurement? Because I can't imagine how stars can form when all things are in...

Can anyone recommend a book(s) that covers these topics: Measure theory / lebesgue integration Hilbert Spaces Distributions PDE's The only material I have is the lecture notes and they are quite difficult to work through. I need to get the basics I think, before I will...

As the title says, I want to measure the angle of a street from true north so I can know what time of the year the sun will align with it.

Hello, I've read about this in four different textbooks and in several websites, but I still don't get it: how are Cepheids used to measure distances? I understand that Cepheids are stars whose brightness varies periodically; that the longer their period, the brighter they are; and that...

Hi all, I apologize now at how elementary this is, but I have been all over google and I cannot get a straight answer. My question seems to me be to be quite easy. Maybe I am over simplifying it. Anyways, any help is much appreciated. Btw, it's been 15 years since my last physics class...

If i have a measurable set with positive measure, how do I prove that there are 2 elements who's difference is in Q~{0} (aka a rational number that isn't 0.

My friend has a 24 HP electric generator and wants to know the number of watts being delivered. My understanding is that the 24 HP refers to the power input to the generator and he wants to know the output power generated. Can someone tell me how to measure it?

Hello, I would like to know what are the differents methods to measure the speed of the light. Thanks :smile:

A book I'm reading says: If a set A has infinitely many points which can be arranged in a sequence a_1,a_2,\cdots,, then A has measure zero. What does it mean by "can be arranged in a sequence"? The book gives an example on the set A which is all the rational numbers between 0 and 1. Why...

For that matter how do you detect the position of particle. Note that I am aware of HUD and therefore am asking you measure them sepretly.