Measure Theory

V. Liskevich
1998

1 Introduction

We always denote by X our universe, i.e. all the sets we shall consider are subsets of X.
Recall some standard notation. 2X everywhere denotes the set of all subsets of a given
set X. If A \ B = ? then we often write A t B rather than A [ B, to underline the
disjointness. The complement (in X) of a set A is denoted by Ac. By A4B the symmetric
difference of A and B is denoted, i.e. A4B = (A \ B) [ (B \ A). Letters i, j, k always
denote positive integers. The sign  is used for restriction of a function (operator etc.) to
a subset (subspace).