Yes, though I would use the phrase "consists of". [latex]f_x maps the set f all real number to the set of non-negative real numbers.

function maps the open interval (-c, c) (all real numbers strictly larger than -c and strictly larger than c) to the set of all real numbers.2) a function

Assuming that "P" here is probability, not "power set", This is the probability that the variable X is any real number other than or .2)

This requires that " " be a set of numbers, some of which may be equal to 1. is the smallest is, less than or equal to 0, such that the with subscript i+ 1 is equal to 1.3) Random variable

says that A is a subset of so this says that a probability measure is a function that assigns a value, P(A), to every subset A of . (Normally a probability is a number between 0 and 1 but that is not stated in your (4) so I just used the word "value".)4) A probability measure on a sample space is a function A P(A) of event