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. Converge(in measure)

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 4 Section 22

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 2. Pointwise Converge

#### Definition

#### Reference

None

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 3. Uniformly Converge

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 4 Section 21

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 4. Almost Uniform Converge

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 4 Section 21

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 5. Weak Converge

#### Definition

#### Reference

Functional Analysis, Sobolev Spaces and Differential Equations, Haim Brezis, Chapter 3

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas

## 6. Converge in the Mean/ Mean Converge

#### Definition

#### Reference

Measure Theory, Paul R. Halmos, Chapter 5 Section 25

#### Related Topics

- Definitions
- Theorems/Corollary/Propositions/Lemmas