Drawing: Definition of Lebesgue Outer Measure

The Lebesgue Outer Measure, or more briefly the outer measure, of a set is given by $m^*(A)=inf \sum l(I_n)$ , where the infimum is taken over all finite or countable collections of intervals $I_n$ (where $I_n = [a,b)$ is bounded) such that $A\subseteq\cup I_n$
G De Barra

While we were thinking about how to construct examples for this definition; a friend came up with this interesting observation:

Step 1: We will collect the coverings of set A.
Step 2: We will find the summation of the lengths of the elements in each covering.
Step 3: We will put all the values what we got in Step 2 in a set.
Step 4 : We will find the inf[imum] for the set we constructed in Step 3.

I was quite excited by her observation. I thought I’ll give it a cartoon twist, to help them learn the definition better.

Visual ~~queues~~ cues to remember things is very useful trick students can leverage to memorize key facts.

In fact, if you have watched BBC’s Sherlock series, you might have heard a term called “Mind Palace” over and over again – that’s an extension of the use of visual queues to remember facts, but takes a lot of practice and meditation to build mind palaces. Read more about it in Wikipedia >>

Another simpler tool you can use to organize your thoughts is called Mind Maps. This is a tool you can master easily. Read more about it in Wikipedia >>

We used to use mind maps to summarize learning in class – do try it out, and get in touch with us if you need any help!

We had talked about some useful computer-aided mind mapping tools in a recent post (link).

Don’t forget to hit the like button below/share this article if you find it interesting! 🙂 If you do like this, do follow the blog for more posts like this!

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This cartoon also reminds me of a very good blog I came across many years ago: Math with Bad Drawings (link). Must confess he’s been an inspiration to me! This recent post (link) there might interest – do check it out!