Sentence examples similar to provided it existed from inspiring English sources

It can be shown that, whenever X has a probability density function, its expectation (provided it exists) is given by equation (15), which remains a useful formula for calculating E X).

For and, we define as follows (provided it exists): (2.1).

We denote the intersecting time by (bar{delta}_{m}) provided it exists.

The intersecting point is denoted as (bar{delta} _{m}) provided it exists.

vanishes for the first time after t > 1. Denote by u ( t, m ) the solution of (1.4 - 1.6 1.4 - 1.6 it exists.

Then one defines to be the number (provided it exists) with the property that given any, there is a neighborhood of such that (2.2).

Denote by the number (provided it exists) with the property that given any, there is a neighborhood of such that (23).

For and, the nabla derivative of at, denoted by (provided it exists) with the property that for each, there is a neighborhood of such that (2.3).

The natural density of (K) is defined by (delta (K =lim _{n}frac{1}{n}|K_{n}|) provided it exists, where (|K_{n}|) denotes the cardinality of set (K_{n}).

For and define the delta (see [10, 11]) derivative to be the number (provided it exists) with the property that for given any there exist a and a neighborhood of such that (1.5).

Assume that is a function and that. is supposed to be the number (provided it exists) with the property that given any ; there is a neighborhood of satisfying (22).