14 Measure
Mr. Samopriya Basu
Objectives
- Measure
- Di erent types of measure
Objectives
- Measure
- Di erent types of measure
- Properties of measure
Objectives
- Measure
- Di erent types of measure
- Properties of measure
- Some examples
Informal Definition
- I A measure on a set is a systematic way to assign a number to each suitable subset of that set Informal Definition
- A measure on a set is a systematic way to assign a number to each suitable subset of that set A measure is a generalization of the concepts of length, area and volume.of the n dimensional Euclidean space Rn
Informal Definition
- A measure on a set is a systematic way to assign a number to each suitable subset of that set
- A measure is a generalization of the concepts of length, area and volume.of the n dimensional Euclidean space Rn
- A particularly important example is the Lebesgue Measure on a Euclidean space, ehich assigns the conventional length, area and volume of Euclidean geometry to suitable subsets
Informal Definition
- A measure on a set is a systematic way to assign a number to each suitable subset of that set
- A measure is a generalization of the concepts of length, area and volume.of the n dimensional Euclidean space Rn
- A particularly important example is the Lebesgue Measure on a Euclidean space, ehich assigns the conventional length, area and volume of Euclidean geometry to suitable subsets
- Measure theory was developed in successive stages during the late 19th and early 20th century.
Measure
- I Let F be the field of subsets of , the reference set. A set function de ned on ( ; F) is called a measure if,
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