Integrability of Real Numbers (R)

Practice Questions

Introduction to Analysis › Integrability of Real Numbers (R)

Questions

6

1

What term has the following definition.

, $b\ \epsilon\ \mathbb{R}$ and . Over the interval is a set of points $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ such that

2

What term has the following definition.

, $b\ \epsilon\ \mathbb{R}$ and . Over the interval is a set of points $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ such that

3

What conditions are necessary to prove that the upper and lower integrals of a bounded function exist?

4

What conditions are necessary to prove that the upper and lower integrals of a bounded function exist?

5

What term has the following definition.

The __________ of a partition $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ is

$||P||=\max_{1\leq j\leq n}|x_j-x_{j-1}|$

6

What term has the following definition.

The __________ of a partition $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ is

$||P||=\max_{1\leq j\leq n}|x_j-x_{j-1}|$

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