Measure Definition and 1000 Threads

Ok So I was told to think about what would happen if you tried measure something with a metal ruler or tape measure in an environment that would cause negative linear expansion; so the ruler gets smaller. How would the accuracy be affected if the tape measure/ ruler was calibrated at a greater...

The WMAP objective is to measure the temperature differences in the Cosmic Microwave Background (CMB) radiation. My question are, 1.How to distinguish all the radiations of 13 billion years ago from others of the latter ones. 2.How the distance of radiation source is measured. Thanks.

Homework Statement As a rough measure of the relativistic "flattening" of the configuration of electric field lines from a moving charge, we might use the angle \alpha between two conical surfaces which include between them half the total electric flux. That is, half the flux through a sphere...

Homework Statement I have to find two methods used to measure the density of a solid material and one method to measure a liquids density Homework Equations n/a The Attempt at a Solution got one method for the solids and have written this but my teacher wants me to find the...

Hello. Let's say we have the quantity f=1/(1+x) where x has no unit of measure. What is the unit of measure of f, once we take f^t, where t can be in years? Thanks

Hello, I have taken the attached filter response graph of filter gain to frequency created in micro-Cap. My cutoff frequency is 1kHz. How can I measure the roll off rate in db/Dec based on this graph ? Perhaps there is a formula ? Any help would be appreciated.

I'm reasonably convinced that physicists know what happened in the universe at certain temperatures: just find out what happens when you reach those temperatures in a particle accelerator. I still have yet to come across the equation that measures the time before the CMB and what the universe's...

What is an induced measure? I have seen the formal definition many times i am trying to get a grasp of this concept. Does an induced measure mean that we can view the measure associated with a random variable as some co-ordinate function defined on R? Is it the cdf?

Is it possible that 2 sigma-algebras could be independent under one measure but not independent under another? Many thanks.

hi i have some troubles to understand something properly: if oberserver A is not moving in his inertial frame and there is some observer B moving relatively to oberserver A with velocity V, then this observer B will measure a different(shorter) time from the one that is measured by observer A...

My question is two fold. 1) I was asked to measure the BW of a LNA (RF2472G). Is this done with a VNA. I have an obsolete model in my lab Agilent/HP 8720ES. 2) Exactly how would you measure the BW of the LNA in general? Using the VNA? Is this a S11, S12, S22, S21 parameter? please help.

Hi all, I am not sure that if I have posted this thread on right place but as the subject is related to the stochastic & measure theory therefore I am posting it here. Well, my question is that in the subject "Preferences, Optimal Portfolio Choice, and Equilibrium" the tutor has used the...

Hi all, I am reading Probability and Measure by Patrick Billingsley, and I am stuck at one example, please help me understanding it. http://desmond.imageshack.us/Himg201/scaled.php?server=201&filename=30935274.jpg&res=landing Ω=(0,1] My question is that how come the A^c = (0,a_1]U(a'_1...

Homework Statement My question is would I be allowed to say, if lf+-\phil<ε/(2\mu(E) then ∫E lf+-\phil<ε/2 Homework Equations E is the set in which we are integrating over. \mu is the measure \varphi is a simple function f+ is the non-negative part of the function f. The Attempt...

I am starting graduate school in applied math in the fall and am trying to decide if measure theory is necessary or important in terms of applied math and if so, what ares of applied math? I have taken two basic real analysis courses through multiple integrals, etc. and would like to focus on...

I am curious how information is measured. For example, if i send a message with the symbol ∏ to Bob and he replies with a string of digits 3.14... Does one message have more information than the other? How does reducibility factor in?

Homework Statement I was wondering if we Let E be some set such that f-1(E) is measurable then so is f-1(E)c.Homework Equations If the set A is measurable then so is its compliment. The Attempt at a Solution I think the statement is true because f-1(E) is just a set and thus its compliment...

question 1: if f is a countably additive set function (probability measure) defined on σ-algebra A of subsets of S, then which of the probability space "(f, A, S) is called events? question 2: define what we mean by algebra and σ-algebra? for this question in the second part do we have to...

Visible light, like sunlight, consists of photons. Each photon has a level of energy (radiant energy) directly proportional to its frequency. Does anyone have any suggestions on any device to measure the frequency of Photon? Thanks in advance for any suggestions

Why do astronomers and cosmologists prefer to use the Distance Modulus instead of -- rather than in addition to -- Bly (billion light-years) or Mpc (mega parsecs)? Being a LOG10 it distorts relative distances. You can find Bly plotted on a graph (but not specified), and even in studies comparing...

Homework Statement I just have a few quick questions about the definition of Lebesgue Measure of a function ( I just want some clarification on what I read in Royden) In Chapter 3 of Royden, An extended real valued function is defined as being Lebesgue measurable if its domain is measurable...

For example the microcanonical ensemble uses a dirac delta distribution on a certain energy shell E, which is not actually a uniform distribution (even on the energy shell), but it comes close. Why is uniformity (in phase space, or a relevant restriction thereof) natural for equilibrium...

is there "cheap" / high productivity way to measure quality of hand tools? I see online a common complaint that widely available tools have become low quality due to offshore outsourcing, cost cutting, corrupt/lying mislabeling of alloys used etc. Conversely, tools of "proven" brands that have...

I've been looking at the measure theoretic definition of a conditional expectation and it doesn't make too much sense to me. Consider the definition given here: https://en.wikipedia.org/wiki/Conditional_expectation#Formal_definition It says for a probability space (\Omega,\mathcal{A},P), and...

Homework Statement Let \sigma (E)=\{(x,y):x-y\in E\} for any E\subseteq\mathbb{R}. If E has measure zero, then \sigma (E) has measure zero. The Attempt at a Solution I'm trying to show that if \sigma (E) is not of measure zero, then there exists a point in E such that \sigma (\{e\}) that has...

How can you measure voltage - my friend confused me. We all know we can do it by a voltmeter but a voltmeter is a galvanometer and we need to know the resistance of the galvanometer and current passing through it to find voltage But to find out resistance we need to know current and voltage -...

The original problem is as follows: IF E,F are measurable subset of R and m(E),m(F)>0 then the set E+F contains interval. After several hours of thought, I finally arrived at conclusion that If I can show that m((E+c) \bigcap F) is nonzero for some c in R, then done. But such a...

If you are unfamiliar with that notation, S(A, B) = (A \ B) U (B \ A), which is the symmetric difference. And D(A, B) = m^*(S(A, B)), which is the outer measure of the symmetric difference. My issue in this calculation is this: outer measure of a set A is defined in terms of a countable...

I know that a charge is discribed in terms of coulombs. But how did they know that an electron has a charge of 1.60217646 × 10-19 coulomb ? by the way , what is a coulomb exactly ? and how did they found or discribed its quantity ? I would like the answer to be in details please . Thanks

The title isn't quite clear, because the question was a little too long. Here it is in full: How to apply length contraction and time dilation to a moving observer to measure the speed of light of a light beam moving parallel to their reference frame. Imagery and familiarity are my...

I was wondering how to calculate the drift of an object that is falling though air. If I know the mass, air density, and velocity of an object that is falling how can I calculate its movement off the center of he drop point. I.E if you looking down on a grid with x and y on the side how many x...

Is there any parameter that represents the chaotic-ness of a system? For example, can we show that a 4-body system is in general more chaotic than a 3-body problem? Thank you : )

Have a look at http://arxiv.org/abs/1202.5039 Degenerate Plebanski Sector and its Spin Foam Quantization Authors: Sergei Alexandrov (Submitted on 22 Feb 2012) Abstract: We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and...

I'm trying to prove, per ex. 5 of section 2.2 of S. Berberian's Fundamentals of Real Analysis, that where \lambda^* is the Lebesgue outer measure, and An is any sequence of (not necessarily measurable) sets of reals increasing to A, then \lambda^*(A_n) increases to \lambda^*(A). As a hint, it...

Hello all! I chose not to follow the given format, as my question is kind of unique. I hate to be one of those people who just create an account for one thread (as I usually try to avoid this), but my situation is quite urgent. I have a project due Friday, in which I plan to take different...

\nabla\timesgrad(f) is always the zero vector. Can anyone in terms of physical concepts make it intuitive for me, why that is so. I get that the curl is a measure of the tendency of a vector field to rotate or something like that, but couldn't really assemble an understanding just from that.

Hi all, i have heard a lot of signal deterioration. so i just wanted to understand if i send a pulse let us say of some 5V and measure it using an oscilloscope and send it through a very lengthy cable and measure the same signal with an oscilloscope can i find that the amplitude of the signal...

Homework Statement Let Ω = [0,1] with the σ-field of Borel sets and let P be the Lebesgue measure on [0,1]. Find E(X|Y) if: Homework Equations X(w)=5w^2 Y(w)= \left\{ \begin{array}{ll} 4 & \mbox{if $w \in [0,\frac{1}{4}]$} \\ 2 & \mbox{if $w \in (\frac{1}{4},1]$} \\ \end{array}...

Help, I need to find a cheap way to measure the speed of a golf ball in a putt putt type of golf hole and view it in real-time on a PC display? Got any ideas? I thought about using a baseball speed radar gun but thought there must be other good way? Any ideas or have you seen something like this?

Homework Statement Let (X,\mathcal{B},\mu) be a measure space and g be a nonnegative measurable function on X. Set \nu (E)=\int_{E}g\,d\mu. Prove that \nu is a measure and \int f\, d \nu =\int fg\,d\mu for all nonnegative measurable functions f on X. The Attempt at a Solution I'm basically at...

Albert Einstein is quoted as having said "Zeit ist das, was man an der Uhr abliest" ["Time is what a clock measures"]. The question is, as per the title of the thread, how exactly does a clock measure time? When considering this question we need to consider a few things; namely: - what time is...

The Borel σ-algebra can be defined on every topological space. Does that mean that every topological space can be turned into a measure space?

I was wondering what were the fundamental physical units of measurement, ie those from which all other units can be derived. To my mind, there are only two things which exist in the universe and from which all units of measurement can be derived : space and matter. The reasoning is as follows ...

Hi, I would like to measure the power give from a source to a transformer and measure the power consume by a RL component. I see only voltmeter and amperemeter in circuit editor, it's not possible de put wattmeter ? Or maybe there's another solution for find the power ? Thanks in advance ;)

As the title says, is it possible? I was thinking that in order for the multimeter to measure resistance, it first provides current and checks the voltage, and then by ohm's law gets the resistance. But would it even be possible to provide current to n-type Si bar or p-type Si bar? I know...

Hi. Under what conditions does the following equality hold? f(x)=\lim\limits_{\Omega\rightarrow\{x\}} \frac{1}{\mu(\Omega)}\int_\Omega f d\mu where \mu is some measure. Being a little more careful, let \Omega_i be a sequence of sets such that \Omega_{i+1}\subseteq\Omega_i and...

I have another thread going right now but I don't want you to refer to that thread. I frankly don't understand what is going on in that thread so please answer my question here. Why do you need to measure the speed of light in both directions for an accurate reading? If I am in an inertial...

Hello guys In my previous tags come up with some molecular description of substances. And it has been suggested that temperature, a degree of hotness or coldness is basically, a direct indication of the average kinetic energy of the molecules the body made of. After a deeper look toward this...

I am struggling with convincing myself that if you equip \mathbb Z with the counting measure m, the L^p norm of measurable functions f: \mathbb Z \to \mathbb C looks like \| f \|_p = \left( \sum_{n = -\infty}^\infty |a_n|^p \right)^{1/p}. I know that any function on \mathbb Z is...

How can the cantor set be uncountable and have zero measure. Couldn't I map the cantor set to another uncountable set that did not have zero measure. I probably don't understand measure or the cantor set very well. Any input will be much appreciated.