This article introduces the concept of finitely null-additive set function relative to the σ– ring and many properties of this concept have been discussed. Furthermore, to introduce and study the notion of finitely weakly null-additive set function relative to the σ– ring as a generalization of some concepts such as measure, countably additive, finitely additive, countably null-additive, countably weakly null-additive and finitely null-additive. As the first result, it has been proved that every finitely null-additive is a finitely weakly null-additive. Finally, the paper introduces a study of the concept of outer measure as a stronger form of finitely weakly null-additive.

Abstract

Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers, Muhammad and his family

The good and pure and after his companions

God Almighty said: ( ) Do they not contemplate the Qur’an? If it had been from other than God, they would have found in it much discrepancy. God Almighty has made the well-being of people and their lives linked to faith in it. So what is the need of people today to return to the Book of their Lord so that they may return to the right path that God intended for His servants so that they may attain sustenance? Security and the good life. How could it not be, when many of the nations of the world no longer see security or stability because their leaders and politic

Extracorporeal Shock Wave Lithotripsy (ESWL) is the most commonplace remedy for kidney stone. Shock waves from outside the body frame are centered at a kidney stone inflicting the stone to fragment. The success of the (ESWL) treatment is based on some variables such as age, sex, stone quantity stone period and so on. Thus, the prediction the success of remedy by this method is so important for professionals to make a decision to continue using (ESWL) or tousing another remedy technique. In this study, a prediction system for (ESWL) treatment by used three techniques of mixing classifiers, which is Product Rule (PR), Neural Network (NN) and the proposed classifier called Nested Combined Classi

The social tolerance is one of the important variables in personality; it helps growth and development of individual's personality. Theories and the students affirmed that social Tolerance affects the society growth and development as well.
The presents study aims:
1. Estimating the social Tolerance for Baghdad College students.
2. Realizing how College students vary in social Tolerance according to:
Sex, (Male, Female) ٍSpecialization (Scientific, Humanity).
3. Realizing the nature of relationship between social Tolerance of College students and father and mother styles. To achieve this research goals the researcher established parameter (scale) for social Tolerance applied to sample of (500) students male and female. Th

In The Name Of God the Most Gracious, the Most Merciful [Should he not know he that created? And he is the one that understands the finest mysteries (and) is well-acquainted] surah Al-Mulk verse No. (14), this Qur’anic verse is one of the pieces of evidence that indicates the suitability of Sharia for the human life, since God Almighty created the creation and he is the best-known concerning the needs of his creation to survive and for life to continue.

One of the key ways for the continuity of human life is Sharia's possession of the feature of suitability for every time and place, and for the whole world, and it is comprehensive to all the details of life and its integrated systems, a systems that comp

The role of internal control is based on the effectiveness of the budget through an analysis of the reality of the budget in the research sample as it was studied in the preparation and preparation stages and the implementation stage. The sample showed that the sample did not comply with what is stated in the Ministry of Finance publication of instructions and ceilings. In the process of preparing and resulting from the occurrence of deviations in large proportions both in the discussion of the Ministry of Finance or when implementation as a low rate of implementation and the absence of allocations for some items, although there is a need for them as well as the transfer of large proportions of transfers both up or down and the purpose o

This study was conducted at the poultry research station to the office of Agricultural Research / Ministry of Agriculture / during the period 4/1/2016 to 5/5/2016 and 336 one-day-old Ross308 chicks were used, and fed on diets provided with dried dill (Anethum gravelens) at levels 0.4, 0.6 and 0.8% for treatments D2, D3 and D4, respectively, and they were compared with the control treatment D1. Each treatment included three replicates in each replicate contain 28 birds, in order to study the effect of adding different levels of dried dill plant on the productive performance and some characteristics of the carcass for broilers. The results showed a significant increase (p<0.05) in the average body weight at 5 weeks of age for the treatments (