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

The Following Materials could also be viewed by

### 1. Measure(on a ring)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 2. Finite Measure

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 3. Complete Measure

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 4. Premeasure

#### Definition

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 5. Measure

#### Definition

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 6. Signed Measure

#### Definition

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 7. Outer Measure

#### Definition

#### Notations

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 8. Inner Measure

#### Definition

#### Remark

#### Reference

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

#### Related Topics

- Definitions
- Hereditary Sigma-Ring

- Theorems/Corollary/Propositions/Lemmas

## 9. Lebesgue Outer Measure

#### Definition

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 10. Lebesgue Measure

#### Definition

#### Remark

#### Properties

#### Reference

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

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 11. Measure Space

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 4 Section 17

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 12. Complex Measure

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 6 Section 28

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas