Measure Definition and 1000 Threads

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...

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.

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'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 [SIZE="5"]CMB observations do not...