## Sekai 🌐 🗺

Sekai is the kanji for 世界, meaning “the world”. That’s a great word because of the scale it designates.

## Mesurabilité des réalisations trajectorielles

### $X: \omega \mapsto X(\cdot, \omega) \in \mathcal{M}((\Omega, \mathcal{A}), (\CO(\Bbb{T},\R), \Bor{\CO}))$

Notations Supposons toutes les notations dans Espace de trajectoires. Problématique La mesurabilité de l’application dans le sous-titre est basée sur l’égalité suivante. $$\Bor{\R}{\OXT} \cap \CO = \Bor{\CO}$$ J’ai passé quatres heures pour comprendre pourquoi ça entraîne la mesurabilité ? pourquoi l’égalité elle-même est vraie ? Réponses Mesurabilité de la trace sur $\CO$ de $\Bor{\R}{\OXT}$ A la première lecture, je ne connaisais même pas la définition de la trace d’une tribu sur un emsemble. [Read More]

## What are Dataframes?

### Understand dataframes from a non-example

Motivation The books that I read in the past didn’t explain what a dataframe meant. Definition Dataframe A table of data in which the values of each observed variable is contained in the same column. Counterexample I’ve difficulty in reading long lines of text like the above definition, so let’s illustrate this definition with a counterexample. We have carried out repeated experiments with four types of things and obtaine some data. [Read More]

## Enlarged /var Partition

### Background

I’ve installed Ubuntu 18.04 on my new laptop.

### Problem

The /var partition was too small. The system complained that only 200 MB was left.

### Solution

1. Rebooted with my live USB.
2. Opened GParted.
3. Moved /tmp partition to the left and grew it to 6 GB.
4. Grew /var partition to 16 GB
5. Click

## Ultrafilters Are Maximal

Ultra filter A filer $\mathcal{F}$ containing either $Y$ or $Y^\complement$ for any $Y \subseteq X$. Two days ago, I spent an afternoon to understand Dudley’s proof of this little result. A filter is contained in some ultrafilter. A filter is an ultrafilter iff it’s maximal. At the first glance, I didn’t even understand the organisation of the proof! I’m going to rephrase it for future reference. [Read More]