In order for convenience in checking definition along learning in Math, I found it necessary to gather definitions of the same kind so that distinguishing the differences among them will no longer be a tedious job. This work is very hard to do even many materials are available, if you want to use for commercial use, please contact me for permission. Furthermore, the work is still long from finished, if you want to contribute for more or better definitions, please contact me.

Tianyu Zhang

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### 1. mu*-measurable

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 11

#### Related Topics

- Definitions
- Hereditary Sigma-Ring
- Outer Measure

- Theorems/Corollary/Propositions/Lemmas

## 2. Measurable Cover

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 12

#### Related Topics

- Definitions
- Hereditary Sigma-Ring

- Theorems/Corollary/Propositions/Lemmas

## 3. Measurable Kernel

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 14

#### Related Topics

- Definitions
- Hereditary Sigma-Ring
- Sigma-Field(Algebra)

- Theorems/Corollary/Propositions/Lemmas

## 4. Lebesgue Measurable

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 15

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 5. Measurable(of a set)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 15

#### Related Topics

- Definitions
- Ring
- Sigma-Ring

- Theorems/Corollary/Propositions/Lemmas

## 6. Measurable(of a function)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 15

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 7. Borel Measurable Function

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 15

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 8. Lebesgue Measurable Function

#### Definition

#### Remark

#### Reference

Measure Theory, Paul R. Halmos, Chapter 3 Section 15

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas