Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Measures in Mathematics


Affiliations
1 Gobindgarh Public College, Khanna, Ludhiana -141001, India
     

   Subscribe/Renew Journal


The current paper presents the concept of measures in mathematics. The terms "measure," "measurable," etc. have very precise technical definitions that can make them appear difficult to understand. Measures are important not only because of their intrinsic geometrical and probabilistic significance, but because they allow us to define integrals. In this paper, we discuss brief theory of measures and their properties. The paper also includes the various important list of examples of the measure that are used in various fields of mathematics. We have used standard definitions and notations from set theory.

Keywords

Measure, Set, Lebsegue.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Bogachev V. I., Measure Theory, Vol. I. and II, Springer-Verlag, Heidelberg, 2007.
  • Cohn D. L., Measure Theory, Birkhauser, Boston, 1980.
  • Evans L.C. and Gariepy R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992.
  • Taylor M. E., Measure Theory and Integration, American Mathematical Society, Providence, 2006.
  • Bauer H., Measure and Integration Theory, Berlin: de Gruyter, ISBN 978-3110167191, 2001.
  • Bear H. S., A Primer of Lebesgue Integration, San Diego: Academic Press, ISBN 978-0120839711, 2001.
  • Bogachev V. I., Measure theory, Berlin: Springer, ISBN 9783540345138, 2006.
  • Czyz J., Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas. Singapore: World Scientific, 1994.
  • Jech T. J., Set Theory, 2nd ed. Berlin: Springer-Verlag, p. 295, 1997.
  • Wheeler R. L. and ZygmundZ, Measure and Integral, Marcel Dekker, 1977.
  • Seth B. R., Generalized strain measure with applications to physical problems, Rep. 1966.

Abstract Views: 142

PDF Views: 0




  • Measures in Mathematics

Abstract Views: 142  |  PDF Views: 0

Authors

Gaurav Verma
Gobindgarh Public College, Khanna, Ludhiana -141001, India

Abstract


The current paper presents the concept of measures in mathematics. The terms "measure," "measurable," etc. have very precise technical definitions that can make them appear difficult to understand. Measures are important not only because of their intrinsic geometrical and probabilistic significance, but because they allow us to define integrals. In this paper, we discuss brief theory of measures and their properties. The paper also includes the various important list of examples of the measure that are used in various fields of mathematics. We have used standard definitions and notations from set theory.

Keywords


Measure, Set, Lebsegue.

References