Getting up early

Dear Sumant,

It's 21:42 and I am updating this from home. I am using my Linux Computer to write this blog. It has Fedora 6 on it. It's amusing that I still have such an old version of Fedora, whereas there used to be time when I would get the newest Linux Operating System as soon it used to be released. However this computer has so far served me pretty well. It's an old Dell Pentium 3 desktop computer. Once my sister had that and she shipped it to me. I just had dinner with Akina at John Taco. I had Vegetarian Salad and Bean Taco. Today two of my classes were canceled including the one I was teaching because of the power outage in Agriculture Building.

I am happy with one thing that today I managed to wake up at 4 am in the morning, so I had time to do Yoga and study. It's no wonder that one can accomplish so many things but just getting up early in the morning. As I have been able to include Yoga and writing into my daily schedule the next thing I need is the morning schedule. I also was able to finish grading for Dr. Wallis and play literati with Kathleen.

Since we have been talking about analysis on this blog. Let me continue that discussion today with (a.e) also called almost everywhere concept in analysis. A proposition is said to exist almost everywhere if the set {x belongs to R:P(x) is not true} has a measure 0. Now two things first what is a proposition, well in mathematics a proposition is just a statement which is either true or false. So what does this definition tells us that the proposition exists everywhere if for some value its zero. Thus two function f and g are said to same a.e if Lebesgue Measure ({x belongs to R: f not equal to g}) is zero.

The other important concept in Analysis I want to discuss is Little Woods 3 Principle.

1. Every measurable set is NEARLY a finite union of open interval

2. Every measurable function NEARLY uniformly continuous.

3. Every convergent sequence of (measurable) function is NEARLY uniformly convergent.

Note the word NEARLY. The 3 principle is also called as Egroff's Theorem. I will give the prove of these some other time.

That's for today

Sumant Sumant