Intuitive Vs Conceptive : Set/Number/Measure Theory + Real Analysis: Lebesgue Measure and Integration

Lebesgue's post-doctory thesis: Measure, length and area;

Joseph Louis Bertrand's three different values of Distribution within three different Sampling Spaces.

Cauchy: Integration Theory: 积分，连续性

Riemann: Derivative Existence Theory: 可导性

Weierstrass: Power Series Theory 幂级数

有些重要历史事件，例D(x)对 Lebesgue的Measure Theory的启发。

Length, area, and volume | measurement, calculation, shapes

BRILLIANT.ORG: Lebesgue Integration | Brilliant Math & Science Wiki

AMS: Lebesgue Measure - American Mathematical Society

MIT: 18.102 S2021 Lecture 9. Lebesgue Measurable Functions - MIT

https://math.mit.edu/~djk/calculus_beginners/chapter16/section04.html

CORNELL: Lebesgue Measure - Cornell University

AN INTUITIVE GUIDE TO LEBESGUE MEASURE - University of Texas

UC Berkeley: The Lebesgue Integral - University of California, Berkeley

HARVARD: Math212a1411 Lebesgue measure. - Harvard University

A User-Friendly Introduction to Lebesgue Measure and Integration, Gail S. Nelson

Dirichlet Function:

狄利克雷函数是一定义域为R实数集、值域不连续的函数。其图像以Y轴为对称轴，是偶函数，

它处处不连续，处处极限不存在，不可黎曼积分。是处处不连续的可测函数。

狄利克雷函数意义:

Measure Theory: D(x) measurable可测度, 但是处处不连续不可导！

Conceptive VS Intuitive mind: D(x)的反直觉！
是数学史上第一位重视概念的人，前人数学研究是直觉主导思维。

但是Intuitive Method始终是人类的一大思维方法论，
在管理决策、政治经济、思想方法、科研等解决未知与不确定性方面上，至今仍有不可取代的作用。