In order for convenience in checking definition along Learning in Math, I found it necessary to gather definitions of the same kind to distinguish the differences among them. This work is very hard to do even many materials are available; so if you want to use for commercial use, please contact me for permission, otherwise. 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. Additive

#### Definition

#### Reference

Measure Theory Paul R. Halmos Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 2. Finitely Additive

#### Definition

#### Reference

Measure Theory Paul R. Halmos Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 3. Countably Additive

#### Definition

#### Reference

Measure Theory Paul R. Halmos Chapter 2 Section 7

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 4. Sigma-Additive

#### Definition

#### Reference

Measure Theory Paul R. Halmos Chapter 3 Section 12

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 5. Subadditive

#### Definition

#### Reference

None

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 6. Finitely Subadditive

#### Definition

#### Reference

None

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 7. Countably Subadditive

#### Definition

#### Reference

None

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 8. Sigma-Subadditive

#### Definition

#### Reference

None

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas