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,