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"The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. "

"Tulisan ini membahas tentang ukuran Borel pada ruang Hausdorff yang kompak lokal dan regularitas ukuran Borel. Selanjutnya jika terdapat koleksi ruang Hausdorff (Xa : a ЄA} yang kompak lokal dan saling lepas, dapat dibentuk gabungan bebas X - U Xa , dengan memberikan topologi yang tepat aeA X akan menjadi sebuah ruang topologi Hausdorff pula . Pada masing-masing X diberikan ukuran Borel yang pada X dapat pula dibentuk ukuran Borel gabungan bebas A/ dari { Ma : a e A } . Tujuan utama tulisan ini adalah nemberikan syarat perlu dan cukup agar ukuran Borel gabungan bebas t-t juga regular."

"This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic."

"Tugas akhir ini membahas beberapa metode Summability Kegunaan metode Summability ini dapat dilihat saat kita menentukan kekonvergensian suatu deret tak hingga, Selain itu juga dapat digunakan untuk menghitung jumlah suatu deret tak. Hingga. Pada pembahasan terakhir akan ditentukan Cesaro Sum mability dari deret fourier."

"This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis, asymptotic constructions of solutions, energy and dispersive estimates, and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. ​"