Measure Definition and 1000 Threads

Not sure where to post about measure theory. None of the forums seems quite right. Suppose that ##(X,\Sigma,\mu)## is a measure space. A sequence ##\langle f_n\rangle_{n=1}^\infty## of almost everywhere real-valued measurable functions on X is said to converge in measure to a measurable...

Can the concepts of measure theory or probability theory be derived from logic in a complete fashion? Or, are the concepts of measure theory merely proven by arguments whose forms are logical? I'm looking to gain a complete understanding of measure theory, and I wonder if that means I have to...

I would like to ask if anybody can help me figure out a fair way to measure the difference of two measurements in percentage. I have two sets of measurements X and Y, and both are data with unknown noise. To measure the difference in percentage of these two, both equations can be used (I...

I'm doing a university project in Sweden where i want to continuously measure the activity in the Bulbospongiosus muscle. Is there any cheap easy method/instrument for doing this or do i need expensive professional medical equipment for this? The main problem i see is how to isolate the...

How does an experimental physicist measure it, without going into too much detail? EDIT: found an old topic on it ( https://www.physicsforums.com/showthread.php?t=227477 ) which wasn't very helpful, so I'll specify more: Is the following procedure a "valid" momentum measurement? Two position...

When I write down a quantum field (for instance to compute T^00 or some expectation value) I write it as an integral over momentum space. If I am working in curved space should this be divided by sqrt [g]? (and why or why not?)

Hi For measuring the casimir effect in a experiment, two conducting plates are set up parallel to each other. As far as I know, in all experiments so far there was always a small electric current induced in both plates. So my question is: Why is this electric current necessary in such an...

What is the difference between a probability mass function and a probability measure or are they just the same thing? Thanks!

How can I measure the chemical potential of a gas (not necessarily ideal), using calorimetry alone? I mean, without knowing any equations of state, being able to measure pressure, temperature, volume, and number of particles. Also, I can add a measured amount of heat energy to the gas using a...

Does anyone have any suggestions on what device can measure sound frequency below 20 Hz? Thanks in advance for any suggestions

Homework Statement Please I need your help in this question. I don't know how to answer it. The question: Show that X ⊂ ℜn has measure 0 if and only if ε > 0 there exists an infinite sequence of balls B_i ={ x ∈ R^n| |x-a_i | < r_i} with ∑ r^{n}_{i} < ε such that X ⊂ ∪ ^{\infty}_{i...

Homework Statement I am looking for an example of a series of funtions: \sum g_n on \Re such that: \int_{1}^{2}\displaystyle\sum_{n=1}^{\infty}g_n(x) \, dx \neq \displaystyle\sum_{n=1}^{\infty} \, \int_{1}^{2} \, g_n(x) \, dx "dx" is the Lebesque measure. 2. The attempt at a solution I...

Does this define "measure"? I've been reading the following paper: Scaled Boolean Algebra, by Michael Hardy, arXiv:math/0203249v1. and I'm wondering how much his efforts prove. He seems to prove that Boolean Algebras (such as exist in set theory and Propositional logic) can be mapped to...

Homework Statement How does one experimentally measure an irregular object's volume given that said object floats on water? The Attempt at a Solution It seems to me that the simplest solution to this is to submerge the whole object by pressing down on it to the point that only the object...

I've been reading about the history of the verification of maxwell's theory, and I'm a bit confused how people in those times could measure such high frequencies. I imagined they used instruments that were much more mechanical, and so I'm not sure how they could know or measure things that...

How can people measure the Hubble's constant using WMAP? I found a journal named First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Determination of Cosmological Parameters http://iopscience.iop.org/0067-0049/148/1/175 In 4.1 said CMB observations do not directly...

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...

Homework Statement Let m be the Lebesgue measure on \mathbb R^d , and define the open sets O_n = \{ x \in \mathbb R^d : d(x,E) < \frac1n \} where d(A,B) = \inf\{ |x-y| : x \in A, y \in B \} 1) Find a closed and unbounded set E such that \lim_{n\to\infty} m(O_n) \neq m(E) . 2) Find an...

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...

Homework Statement If m*(E)=0, then m*(E^2)=0. The Attempt at a Solution I have observations which may or may not make sense. Obviously we have that {Ik} is a cover of E. So we want {I2k} to be a cover E2. I have a chain of inequalities which may/may not make sense. 0 = m*(E)...

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.