Measure Definition and 1000 Threads

I’m an electrical engineer. When explaining gravity in GR terms to my peers, and I get to the part about there being no net force acting upon an object that’s “free falling” in curved spacetime, I have difficulty countering the argument: “Yeah, you can’t measure a net force because gravity is...

Homework Statement can we measure time and accelaration at the same time? what exactly acceleration operator is? Homework Equations heisenberg's uncertainity principle The Attempt at a Solution I guess acc. operator is dp/dt i.e. \frac{\partial^2 }{\partial t \partial...

today i interviewed for a job and the guy said i need a 100' tape measure in tenths...what the hell does that mean? also, how does one go about using one?

How important is a measure theory course as an undergrad? I have to choose between taking an undergrad measure theory course and doing research. I'm already doing another research project, but I figure no grad school is going to penalize me for doing too much research. But how "bad" is it that...

if m(.) is a non-atomic measure on the Borel sigma-algebra B(I). I is some fixed closed finite interval in R. How to show that f satisfies the following: m(S) = L(f(S)), S in B(I) where L is the Lebesgue measure and f(x) = m( I intersect(-infinity,x] )

Homework Statement If f:[a,b] -> C is the uniform limit of step functions (f_n) on [0,1], show that f is Lebesgue integrable My first question is why on [0,1] and not on [a,b]?

Homework Statement m((a,b])=b-a is defined as the lebesuge measure what is m([a,b))? The Attempt at a Solution m({a})=0 for any a in R? so m([a,b))=m((a,b])?

Homework Statement Consider a measure f mapping from a family of sets A to [0,infinity] Let the measure be finitely additive and countable subadditive. Prove that f is countably additive on A. The Attempt at a Solution To show equality from an inequality we do ie. a<=b>=a so...

Homework Statement A, B in a sigma algebra Prove m(A)+m(B)=m(AuB)+m(AnB) m denotes the measure. The Attempt at a Solution Don't see how to do it. Somehow we are dealing with each individual set and taking the measure on them. Then finding what they equate to.

DISCLAIMER: i may very well have exactly zero idea what I'm talking about. please feel free to berate me if i am way off base... so i know the doppler effect is normally used to determine an unknown radial velocity, but I'm assuming that if i know the velocity of the source, i can use the...

I understand that the range of extreme temperature is from 0-15million K. What are the ways that we can measure this? How did they figure out the temperature of the sun? thermocouple thermometer? blackbody radiation? optical pyrometer? I've tried searching for general information on these...

hi guys... i quiet new here... just wondering ,.. how to measure a inductor... TQ

MEASURE To measure nature with absolute certainty, one would need a tool of absolute certainty. Unfortunately for science, there is no such thing! Measure? MJA

I am still a high school student and I want to do an experiment on a solar panel. I want filter out red light and then focus is it onto a solar panel and measure various intensities and how it relates to the variation of power output from the solar panel. For this I suppose I should measure the...

Would I be correct in thinking of time as the measure in length of a single point. If we take into account one second of this measure of time, would a photon be the longest and the shortest a cesium atom? Would I be correct in thinking of space as the measure in length between two points...

Is it too hard to devise objective measurements can you measure happiness? what is possible?

What is the Lebesgue measure of the Mandelbrot set?

Okay, a meter is the distance traveled by light in 1/299792458th of a second. It's relative, so the actual measure of a meter changes depending on your velocity (I won't even go into "Relative to what?", though I do sort of wonder if one could find a 0 point of velocity by measuring light going...

I used to be really good at measuring stuff and all in projectile.But after a while i forgot how to measure the Voy(initial vertical velocity) si it like Voy=Vo sin(0[angle sign]) but how does an object with an initial velocity of 50 m/s and an angle of 30 degrees have an Voy (or Vy) of 24.99?

Could anyone recommend a piece of lab apparatus which will measure the volume of an irregular object? I cannot use displacement of water as the object will compress under pressure and I suspect submerging the object in water will give a different displacement from the actual volume at 1 atm...

Homework Statement A spring that can be considered ideal hangs from a stand. Suppose the spring is used in a spring scale that is limited to a maximum value of 25 N, but you would like to weigh an object of mass M that weighs more than 25 N. YOu must use commonly available equipment and...

hi, as part of a project me and my friends are undertaking we are trying to measure the change in resistance of an electromagnet when a coin is placed near near the electromagnet. i have been trying to use a bridge rectifier to convert the system to DC but i have been encountering a few...

does a set with empty interior have measure zero? I think it does...

Can someone show me an example to clarify this statement from Royden's Real Analysis: The Lebesgue measure restricted to the sigma-algebra of Borel sets is not complete. Now, from the definition of a complete measure space, if B is an element of space M, and measure(B) = 0, and A subset of...

Homework Statement Let \mathscr{X} be a set, \mathscr{F} a \sigma-field of subsets of S, and \mu a probability measure on \mathscr{F}. Suppose that A_{1},\ldots,A_{n} are independent sets belonging to \mathscr{F}. Let \mathscr{F}_{k} be the smallest subfield of \mathscr{F} containing A_{1}...

How does one measure the index of refraction of a liquid, more specifically the angle of refraction? I'm finding it's relationship to temperature. I can't just dip the protractor into the liquid( as a test medium I used water compared to air) and measure the angle that is in the water(either...

Hi, I'm just reading Rudin's Principles of mathematical analysis - the last chapter on Lebesgue integration and I am having a bit trouble understanding the motivation of the definition of Lebesgue measure. This is how I understand it: We want to measure sets in \mathds{R}^n so what we...

Let be a Lebesgue integral with a measure M on the interval (a,b) so: \int_{a}^{b}dMf(x)=I(a,b,M) We don't know or can't say what M (measure) is , however my question is if we had a trial function U(x) so we could calculate I(a,b,M) for this U without recalling to the measure,either by...

hi all! I was just thinking about organic compound indicators, and biuret solution for proteins crossed my mind. I know that it can be used to qualitatively tell the presence of proteins (peptide linkages) with a colour change. But is there a way that biuret solution can be used to take...

1.A concrete column has a diameter of 350mm and a length of 2m. If the density (mass/volume) of concrete is 2.45\frac{Mg}{m^3} determine the weight of the column in pounds The answer is given as 1.04 kip: What is or what unit of measure is a kip?

Homework Statement Given is the measure space (A,\mathcal{P}(A),\mu) where \mu is the counting measure on the powerset \mathcal{P}(A) of A, i.e. \mu(E)=\#E I have to show that if \int_A f d\mu <\infty, then the set A_+=\{x\in A| f(x)>0\} is countable. 2. Relevant theorems I wish I knew...

1. The problem statement Let (X,M,\mu) be a measure space and let f:X \to [0,\infty] be a measurable function. Now define for E\in M the following function: \mu_f (E) = \int_E fd\mu Show that \mu_f is a measure on M. The Attempt at a Solution I will skip the part where I have to show that...

Hi, this is not a homework problem because as you can see, all schools are closed for the winter break. But I'm currently working on a problem and I'm not sure how to begin to attack it. Here's the entire problem: Let f be bounded and measurable function on [0,00). For x greater than or...

I am in grade 11 physics and haven't yet learned about thermodynamics or anything dealing with heat really. I am wondering basically if you can reliably measure the power difference between two settings on a stove through temperature. i.e use a thermometer, measure the temp of the element at...

It is a fact that Lebesgue measure is characterised uniquely by the five requirements: 1 - measure of empty set = 0 2 - monotonicity 3 - measure = length for intervals 4 - translation invariance 5 - countable additivity It is also true that Lebesgue outer measure satisfies: 1 -...

I saw this come up in a proof: Since A is a Jordan measurable set (bd(A) has measure zero), there exists a closed rectangle B s.t A subset of B. So basically theyre saying, if bd(A) has measure zero then A is bounded. Can someone give me a quick proof of that? By the way when i say a set S has...

how does it work?? i am really too confused and can't understand its idea. can anyone help??:confused: :confused:

If E is a non empty set and (B_n)_{n \geq 1} are elements in the set 2^E. I then need help showing the following: lim_n\, sup\, B_n\, =\, lim_n\, inf\, B_n\, =\, \bigcup_{n\, =\, 1} ^{\infty}\, B_n if and only if B_n\, \subseteq\, B_{n+1}, for all n\, \geq\, 1, Also I...

Definitions If X is a set, an algebra A on X is a non-empty collection of subsets of X which is closed under complements with respect to X, and finite unions. Given an algebra A, a premeasure on A is a function p\, :\, A \to [0,\, \infty] such that: a) p(\emptyset ) = 0 b) If B is a...

When someone says their transistors are a "90nm process" (or similar) I always assumed they meant the minimum gate length their fabrication process could produce. But then while reading this: http://www.intel.com/technology/silicon/65nm_technology.htm I saw this: "Intel's 65nm...

Sorry if this is kind of vague, but the other day, one of my math profs told me about a theorem which he thought was particularly interesting. I might be missing or getting a condition wrong, but here goes: Suppose I(f, d) is a real-valued function, where f is a real-valued function always...

Yep its me again, with another dumb question. Say you have a set I with an ultrafilter F on it. Now I came across the following in a text on nonstandard analysis: let m be the measure induced by F defined as m(A) =1 if A is an element of F and zero otherwise. I know this is going to be...

Quick question. If i pass into a trig function something like cos(3pi*15 seconds), do I drop the seconds from the resultant answer since it's not a valid unit of measure for theta?

Let m be a measure on the space X. I'm told that if m(X)=1, K is a compact subset of X with m(K)=1, and K has the property that any proper compact subsets of K have measure strictly less than 1, then K is called the support of m. Then I'm asked to show that every compact subset of R is the...

what is the formula to measure how fast a bullet can go?

ok, Don't know if this is the right forum, but I'd like some help with this I'm making a project that needs to read acceleration in any direction. I have a 3 axis accelerometer, who's orientation is random, unknown, and changing. So my question is, is it possible to read 2 forces of...

Hello, I'm trying to determine the level of order of a pattern of particles on a sample surface. One idea was to calculate the mean distance between one particle and those adjacent and compare them to the idealised (perfect grid arrangment) distance if I take the area of the surface divided by...

I want to prove that if E is a subset of F and both E and F are measurable, then m(E) </= m(F). (where </= is less than or equal to). Now I figured that I'd use one of the axioms for a measure to prove this, namely If A_i are measureable and disjoint A_n n A_m = {} for n not equal to m...

If I have a sigma-algebra, A, consisting of subsets of X where X = {1,2,3,4}, and I also have a measure on A such that m({1,2}) = 1 m({1,2,3}) = 2 m({1,2,3,4}) = 3 Then my question is this: Is the set E = {3} a member of the sigma-algebra? I figured that since a subset E of X is in...

When drawing sewer pipes, I often include the height above sea level within one centimeter to get the correct fall, simply cause I've been told to do so. I'm just curious as to how this height is actually measured by the people who actually lay these pipes? Is there some kind of instrument that...