Measure theory

1. What is measure theory?
2. What is the use of measure theory?
3. Is measure theory hard?
4. Who invented measure theory?

What is measure theory?

Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and Lebesgue measure, but other examples are Borel measure, probability measure, complex measure, and Haar measure.

What is the use of measure theory?

Measure Theory is the formal theory of things that are measurable! This is extremely important to Probability because if we can't measure the probability of something then what good does all this work do us? One of the major aims of pure Mathematics is to continually generalize ideas.

Is measure theory hard?

The answer is utterly trivial in the measure theoretic formulation of probability, but very hard to express in terms of cumulative distribution functions. Similarly, convergence in distribution is really hard to work with in terms of cumulative distribution functions but easily expressed with measure theory.

Who invented measure theory?

Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon, and Maurice Fréchet, among others.