Measure Definition and 1000 Threads

Hi, I'm currently trying to teach myself some measure theory and I'm stuck on trying to show the following: Let (X,M,\mu) be a finite positive measure space such that \mu({x})>0 \forall x \in X . Set d(A,B) = \mu(A \Delta B), A,B \in X. Prove that d(A,B) \leq d(A,C) + d(C,B) . Could...

Hi everybody, I need to indirectly measure the high voltage across a wire, which is one of the leads to a spark gap. I ran the wire through a coil inductor(air core) and measured the voltage across the coil leads with an oscilloscope when i get the spark. I also connected a resistor in series...

Hi, I have few alternators(one is 3phase), and I want to test the current generated for each alternator at a same rpm. however, what is the proper way of doing this? what is the connection should be? is there a need to convert them to DC, and charge to the battery while testing? or any other...

Hey everyone, I am integrating something (specifically 2-forms, but I think this is a general statement) over a set B of (real) codimension 2 in a 4-manifold (CP_2). I've been told that the measure of a set of codimension 2 will vanish, but I don't really understand why. I've been...

I am confused about lebesgue measure. I have heard that the lebesgue outer measure of the rational numbers is 0. So could someone please give an example of a set of open intervals such that: a. The union of these intervals contains the rational numbers on [0, 1] b. The sum of lengths...

Hi all, How to measure the tangential component of velocity of receding starsor quasars? I ask this because i think the velocity determined by observing the red shift will give only the radial component...won't Thnx for replying...

Hi all, How to measure the tangential component of velocity of receding starsor quasars? I ask this because the velocity determined by observing the red shift will give only the radial component... Thnx for replying...

When a star or galaxy etc is said to be 10 light years away is that from a standard Earth's velocity distance (ie without length contraction) or do we take into account Earth's velocity and gravitation and have a standard length (maybe accordance with the milkyway being stationary or if we...

Problem: f_{n}\rightarrow f in measure, \mu(\left\{f_{n}>h\right\})\leq A Prove that \mu(\left\{f>h\right\})\leq A. My Work: Suppose not, then \mu(\left\{f>h\right\}) > A. From the triangle inequality for measures we get \mu(\left\{f>h\right\}) =...

Hi, I am interested in using an accelerometer to calculate the speed of a car. The accelerometer is a triaxial one and gives 3 values of acceleration; x y and z. These can be assumed to be accurate as i have already worked on the calibration of these values so that they come out in gs. Is...

how we can measure the speed of the electron in an electric field

Let K\subseteq\mathbb R is a compact set of positive Lebesque measure. Prove that the set K+K=\{a+b\,|\,a,b\in K\} has nonempty interior.

Hi! Im measuring how much wood expands in different temperatures using a strain gauge. do i need to use a wheatstone bridge circuit schematic? or else how do i heat up the wood without spoiling the strain gauge. Actually how will i heat up the wood anyway? Also how would i draw a diagram to...

Hi I need to measure the small changes in resistance of a strain gauge. I have read that a wheatstone bridge circuit is used to do this.. but I don't understand why I can't just use a milliammeter to measure the change in current through the strain gauge and then use R=V/I to find the new...

If E_1, E_2, ... is a sequence (of subsets of R^n) that decreases to E (i.e. E_m+1 is a subset of E_m for all m, and E = intersection of all the E_m's) and some E_k has finite (lebesgue) measure, i.e. lambda(E_k) is finite it is a known result that the measure of E is equal to the limit of...

Homework Statement Homework Equations The Attempt at a Solution I'm pretty clueless as to what's going on here. If someone can just please lead me in the right direction, I would be quite grateful.

How do we measure a quantum particle's momentum?

you are in a plane flying east with a head wind of 10 kph. The speed of the plane is measured by measuring the wind speed outside the plane and then adjusting for any head wind. Let's say you get a result (after allowing for the head wind) of of 200 kph. Unbeknownst to you the arm of our...

Do the neutrino detectors measure only the number of events but not the energy of the detected neutrino?

My skill with proofs and number theory is very limited and my use tends toward the stereotyped physicist. Dealing with infinities and identifying exactly what assumptions are in play has become somewhat an issue for me though. My questions are contained in the following visual tool. Please slap...

It is certainly within the realm of rational scientific inquiry to ask, not simply what a clock measures, but it what manner it measures. These are contextual to an experimental science. 1) In common to all clocks, how do clocks measure time? 2) Are there any clocks (that one actually...

Homework Statement A loop of wire is at the edge of a region of space containing a uniform magnetic field B. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area A of the coil inside the magnetic field region is...

All clocks measure the intrinsic motion of matter using a counter to assign a number to the present at the arbitrary rate of one per second. This allows us with a calendar, a circular table or chart, to relate to the past and plan for the future. This makes me wonder about matter, and how it...

A metal disc is placed in a uniform magnetic field of flux density,B,acting through the plane of the disc at and angle,\theta.When the dis is rotated an e.m.f. is induced between the centre and the rim of the disc. http://img158.imageshack.us/my.php?image=scanlc2.jpg Design an experiment...

Hi There! I have a bit of a problem... I work in Audio Visual and install video matrix systems. We are findind that the newer LCD screens are throwing out so much IR interference that they are blocking the Remote Controls from operating the Sky Boxes... The manufacturer of the matrix...

What's a well written textbook on this topic? A textbook that has about the same exposition as Munkres Topology.

1.A rectangular loop and a Circular loop are moving out of a uniform magnetic field to a field free region with a constant velocity V.In which loop the induced e.m.f is constant during the motion of the loop. 2.Name two Physical quantifies other than velocity,wavelength and C,associated with...

Since everything in the universe is moving relative to the other, how can one measure an absolute velocity? Therefore, how can the speed of light be absolute?

Could someone perhaps explain how a potentiometer can be used to measure an unknown emf? My book gives a bad explanation...

Hi all, I need to find a way to measure the capacitance of a mems parallel plate capacitor, can anyone tell me some help on this? The professor suggested a ring oscillator, can someone tell me how can a ring oscillator measure capacitance? I don't have much background on circuit parts, so I...

[SOLVED] The "support" of a measure Posting a problem like this might help me get off my arse. This is #11 / chapter 2 of Rudin's Real and Complex Analysis. Homework Statement Let m be a regular Borel measure on a compact Hausdorff space X, assume m(X) = 1. Prove that there...

dear all can anyone tell me.. if i have a transmission line passed above a metalic surface, there will be a parasitic capacitance between the line and the surface. and it induces interference how can i measure it. and if there is any refrenece about the allowable induce voltage...

In an experiment, do we measure the eigenvalue or the expectation value ? If both can be measured, how can we distinguish one from another ?

Find a function f such that f is in L^P(R) but not in L^Q(R) for p not equal to q, where R is the set of real numers. I'm guessing I need to find a function that only blows up when it is raised to the qth power, but I am having some difficulty proving this.

Just thought for food (not exactly a homework question). Find a Borel subset E of [0,1] such that for any subinterval I of [0,1], 0 < m(E \cap I) < m(I). If you know the answer, post it. Otherwise, I'll post it when I figure it out.

in f to V converter, input is frequencies . Is that electrical or Mechanical frequency?

Hi Guys, Sorry for dumping this thread in here, I really wouldn't know where this would fit... I'm a farmer in Australia and I'm trying out these really simple devices to measure nutrient levels in my soil, they're basically a ceramic container with a small hose that gets buried into the...

[SOLVED] measure zero and differentiability Homework Statement I proved in the preceding exercise the following characterization of measure zero: "A subset E of R is of measure zero if and only if it has the following property: (***) There exists a sequence J_k=]a_k,b_k[ such that every x in...

What kind of tools would I need to measure a specific nutrient from foods I buy with no labels on them, or foods I bake? I.e. I want to test the protein quality, kind of fats, or magnesium in the food per 10g serving. Is it even possible for a normal person to do this as little hobby?

How is measure theory associated with number theory, if at all. If they are connected, can anyone give a link?

Hi there, I am currently looking to measure the tensile strength using Young’s Modulus for steel and brass. My results I have obtained are comparable with published values of E. My question is regarding the formulae, the one I used was: E = F/x X l/a Where a is the original cross section...

Hi all, This is a weird question, I want to measure angles in terms of 360 degrees and not 180. The two lines will share a common point such that Line A ends at the point where Line B begins. In order to do this don't you need to define some sort of "standard" so that you can know...

Hi, I am currently doing my 4th year honours project and i am having a bit of trouble with one of the aspects of it. i have designed a test rig that simulates the motion of waves and from the test rig i have a wire leading down to an anchor point on the floor (a 5kg weight) , and i need to...

Homework Statement An experiment to determine the specific heat of a gas makes use of a water manometer attached to a flask (the figure below ). Initially the two columns of water are even. Atmospheric pressure is 1.4 x 10^5 Pa. After heating the gas, the water levels change to those shown...

Could someone explain to me why we use a gauge-invariant and diffeomorphism-invariant measure on the quantum configuration space? Is it because we want the inner product to be invariant under gauge transformations. What is a gauge-invariant measure anyway? see http://arxiv.org/abs/hep-th/9305045

please help! I need to know the measure of elevation of Antares at 30minute intervals from 7pm to 10.30pm. It's for an assignment and I don't have any idea how to do it. =( Any help at all would be very very very much appreciated.

Has anybody ever heard of some mathematical application of negative probabilities ? What problems arise from allowing negative probabilities ? Of course I know it is counterintuitive, but is there any chance for a reinterpretation of probability (maybe resulting in something very different) that...

I am studying the abstract theory of measure and I was wondering how the Lebesgue case for real functions of a real variable arises. But I did not find it. In the original theory of Lebesgue, a function f:E-->R was said to be measurable if for every real constant b, the preimage of ]-\infty, b]...

Homework Statement Find the peak current in the circuit config: V1 = 15v amplitude, 1khz freq. R = 1.5k Vd = 0.7v Draw the transfer characteristic. http://img341.imageshack.us/img341/9761/picture2ge7.jpg Homework Equations The Attempt at a Solution Transfer Characteristic...

Money is a very powerful and quantitative tool to measure relationships. Here's my logic. Your loved one is sick and about to die. The doctor says, there is a medicine which would cost you $5, can save his/her life or extend the life for one more year. I'm sure most of us would buy the...