Measure Definition and 1000 Threads

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with the proof of Result 2.7 ... Result 2.7 and its proof read as follows: In the above proof by Axler we read the following: " ... ... Thus ... ##\mid t +...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with the proof of Result 2.7 ... Result 2.7 and its proof read as follows: In the above proof by Axler we read the following: " ... ... Thus ... $\mid t + A...

I am reading N. L. Carothers' book: "Real Analysis". ... ... I am focused on Chapter 16: Lebesgue Measure ... ... I need help with the proof of Proposition 16.2 part (i) ... Proposition 16.2 and its proof read as follows: Carothers does not prove Proposition 16.2 (i) above ... Although it...

I am reading N. L. Carothers' book: "Real Analysis". ... ... I am focused on Chapter 16: Lebesgue Measure ... ... I need help with an aspect of the proof of Proposition 16.1 ... Proposition 16.1 and its proof read as follows: In the above text from Carothers we read the following: " ... ...

I am reading N. L. Carothers' book: "Real Analysis". ... ... I am focused on Chapter 16: Lebesgue Measure ... ... I need help with an aspect of the proof of Proposition 16.1 ... Proposition 16.1 and its proof read as follows: In the above text from Carothers we read the following: " ... ...

I am reading N. L. Carothers' book: "Real Analysis". ... ... I am focused on Chapter 16: Lebesgue Measure ... ... I need help with an aspect of the proof of Proposition 16.1 ... Proposition 16.1 and its proof read as follows: In the above text from Carothers we read the following: " ... ...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with proving that the outer measure of an open interval, \mid (a, b) \mid = b - a Axler's definitions of length and outer measure are as follows: Can someone...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need further help with the proof of Result 2.14 ... Result 2.14 and its proof read as followsIn the above proof by Axler we read the following: " ... ... To get started...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need further help with the proof of Result 2.14 ... Result 2.14 and its proof read as follows In the above proof by Axler we read the following: " ... ... To get...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with the proof of Result 2.14 ... Result 2.14 and its proof read as follows: In the above proof by Axler we read the following: " ... ... We will now prove by...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help with the proof of Result 2.14 ... Result 2.14 and its proof read as follows: In the above proof by Axler we read the following: " ... ... We will now prove by...

I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 1: Measures ... I need help with the proof of Result 2.5 ... Result 2.5 and its proof read as follows: Now $$ \mid A \mid \leq \sum_{ k = 1 }^{ \infty } l(I_k)$$ follows from Axler's...

We relating to an electromagnetic radiation as waves. and in waves there is maximum point and minimum point but when there is permanent electromagnetic level there is no disorder or weave . so is it possible to measure it in blank space relative to other places

Least count of the screw gauge = Pitch÷No. of divisions on circular scale=1.5÷100 mm =0.015mm According to me,in this case the main scale reading should be taken as 2 mm because it is the one which is visible and circular scale reading should be 76. So, Diameter=2 mm + 0.015×76 mm = 2 mm + 1.14...

we know that all emission from asctrophysical context is doppler shifted. So, how to make sure the doppler shifted 21 cm not contaminated by some other emission?

Suppose ##\nu## is a measure on some ##\sigma##-algebra ##\mathcal{A}##. Then we must have for all ##A \in \mathcal{A}## either ##A## or ##A^c## is finite, but not both. Because otherwise ##\nu(A)## is undefined or not well defined. I've verified that ##\lbrace \emptyset, X \rbrace## and...

Attempt at solution: We have ##\sum = \lbrace B \subset \mathbb{R} : b \in B \Rightarrow -b \in B \rbrace##. Clearly, ##\emptyset \in \sum##. Let ##B \in \sum## and ##a \in B^c##. Then ##a \not\in B## which implies ##-a\not\in B##. So ##-a \in B^c## i.e. ##B^c \in \sum##. Lastly, for any...

In book Quantum computing explained by David Mahon concurrence, as a measure of entanglement is defined as C(\psi)=|\langle \psi|\tilde{\psi} \rangle | where ##|\psi\rangle=Y \otimes Y|\psi^*\rangle## or with density matrix ##\rho(Y \otimes Y)\rho^{\dagger}(Y \otimes Y)##. Could someone explain...

Hi, I've been reading about radiation detectors (manly form Knoll's book), but there is something I don't understand. Radiation detectors are of very different nature, but they all share a common process to detect a type of radiation: - I have a control volume - The incoming radiation interacts...

Why do they say temperature is a measure of average kinetic energy how is this possible. how can we take it is it applicable for all types of gases?

I am not sure about a, but i think as long as there is no torque about the Lp direction, it will remain constant with relation to the polar star. I would like help in proof this mathematically. I just don't know how to proceed, i wonder if i would need to consider the torque provide by...

I feel like i am spinning my wheels at the start here. so I figured that i would start with some type of wire loop that I could change its diameter. This would allow there to be a change in flux through the loop creating a current through the wire. i could then read the current through the...

I read the proof here: https://proofwiki.org/wiki/Measure_of_Empty_Set_is_Zero that the measure of the empty set is zero.

I want to know between which two quantities of energy, momentum, and mass there is an uncertainty principle going on. Can I measure any two of those at the same time? If yes, which ones? Thank you in advance

How can I measure the terrestrial tide on my place? Since i don't have a MEMS gravimeter or a laser spectometer what will be the simplest method to measure the local Earth tide variations?

Hello! I have a volume of 50 liters which I pressurize with air so that I read 1 bar on the manometer. But there is a leakage in the volume so after 30 sec the manometer shows 0,5 bar. What is then the air flow ( liter / min) of the leakage?

Hello everyone ! I have to built a coffee machine with a coffee tank (instant coffee) and a sugar tank. I'd like to measure a certain quantity of those grains. First, I wanted to make a physical model to know the debit of the grains. But I noticed that it depends on many things like the...

Hi, I am a bit out of my league here, but had a question. I have 5 pieces of .25" thick foam/padding of different densities, and I wanted to measure which one absorbs the most energy (weakens the impact) when struck by a fist/punch or even a ball, how would I do that? I ran across a...

I am in pharmacy school and my professor recently went over lung diseases with us. An important (and cheap) tool that many patients can use to detect whether their lung function is declining is a peak flow meter, which tells the patient how much air they are moving when they exhale with as much...

So, pretty much I want to make an experiment in order to get the speed of light. What I plan to do is to have a lantern in the dark(initially off) perpendicular to a wall, two sensors(one closest to the lantern and the other closest to the wall), then turn on the light making sensor 1 go off as...

i am planning to measure the back emf produced by inductor when you open a switch. i know it is very hard to predict the voltage. but is there any way to narrow the possibilities?

Solving for t' by substitution I obtained t' = 7/8. Then I substituted x= 10 and t = 7/8 in the given equation. Is that the right way to do it? My answer key says the answer is 100 but I am getting 78.5.

First of all this is a question that I had while reading some concepts of my book, so this isn't a homework question. I have started reading the thermochemistry chapter of my book, and it shows the story of Hess' Law and says that it was created is because a calorimeter can't be used to measure...

Summary: Cost-effective ways to measure the swell of elastomers of submersible pumps after they are pulled from wells Dear Physics Community! I am working for an energy company and we are using progressive cavity pumps (PCPs) for producing water from our wells. This is a youtube video...

As indicated in the title and summary, I'm wondering if there is any large scale astronomical effort to assess directly the universal spatial expansion assumed by the Doppler interpretation of the redshift/distance relationship, by measuring individual galaxy subtended angles over time. The...

Summary: I need to build an asymmetric capacitor, but the mathematics of electromagnetics become too tough, do you have any info that can help? Appreciate it! Hello, I am an undergraduate student in engineering and I want to build an asymmetric capacitor, so I need electromagnetics which I...

I am new to photodetectors. I know there are usually two concepts of bandwidths of photodetectors, i.e the spectral and electrical. What I do not understand is the electrical bandwidth. The electrical bandwidth is used to calculate the shot noise of a photodetector. However, the papers usually...

I don't know in which category this subject belongs to. Anyways, here it is: https://www.sciencealert.com/a-new-study-backs-up-claims-that-sound-waves-really-do-have-mass-after-all?fbclid=IwAR2Cmsxm_Garm0PVn03f4UxVQ8adcK4Il3A_N7bUbJT1KaGR1ZfCbGuWVLE How exactly is this measured? Can we expect...

What sensor to would i use to measure the difference in wave length periods. I want to make a rendered image of somthing that field of view that is being obstructed.

I was looking at things today and read (on wiki) that the use of Thompson Scattering reveals electron temperature in a plasma, not ion temperature. I thought that's how ion temp was measured (or maybe it is and the wiki text was incomplete)? Could someone please clarify how ion temperatures in...

I'm trying to learn about Abstract Wiener Spaces and Gaussian Measures in a general context. For that I'm reading the paper Abstract Wiener Spaces by Leonard Gross, which seems to be where these things were first presented. Now, I'm having a hard time to grasp the idea/motivation behind the...

NOTE: this is a programming exercise (Python). I started adding to ##x_{true}## an error related to a (for example) 10% relative error, obtaining ##x_{measurement}##. Then i computed ##y_{measurement}##. To find the precision, i calculated ##(y_{true}-y_{measurement})/y_{measurement}##. If it is...

Hello, I've known about average laser rangefinders that we can use for domestic needs. They're relatively cheap and can measure up to 50 meters but that's about it. However, I've read that military laser rangefinders are able to measure distances using light up to 20 kilometers. How is that...

Hi I am sitting with a homework problem which is to show if I can actually integrate a function. with 2D measure of lebesgue. the function is given by ##\frac{x-y}{(x+y)^2} d \lambda^2 (x,y)##. I know that a function ##f## is integrable if ##f \in L^{1}(\mu) \iff \int |f|^{1} d \mu < \infty##...

Summary: The main idea of my graduation project is to convert the motorcycle engine to work on compressed air that come from a 180 L tank (10 bar compressed air inside the tank ) I have some problems to how calculate the required torque to move the cart . The main idea of my graduation project...

I have a project to create a program to predict tsunami possibility by gathering data and finding pattern from previous earthquakes. It would be using neural network. But I don't really know what I should consider from the data. Is it the magnitude that cause the tsunami? Or is it the depth...

I have a servo motor which rotates 180 degrees. I want to calculate torque of the motor. To calculate the torque I'm thinking of lifting a load of a known value, with a known angular velocity. But I am struggling to find/calculate the torque based on these values. Does anyone know how to do this...

Found myself wondering about this recently, though I can't recall the context. When Mendeleev proposed the periodic table of elements, I believe that it was known that atomic weights of the known elements were multiples of hydrogen's atomic weight. Presumably also with substances like oxygen...