probabilitymeasurepreserving
The term "probability measure" refers to a function that assigns a probability to every measurable subset of a sample space. A sample space, often denoted by $\Omega$, is the set of all possible outcomes of a random experiment. A probability measure, typically denoted by $P$, is a function that maps events (measurable subsets of $\Omega$) to real numbers between 0 and 1, inclusive.
For a function $P$ to be a probability measure on a sample space $\Omega$ with a sigma-algebra
The concept of a probability measure is fundamental to the mathematical theory of probability and statistics,