Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Last week 1. We showed that λ ∗ is σ -additive on M . 2. Hence λ ∗ | M is a measure! We denote it simply by λ . 3. We started on general measure and (a little) integration theory. 4. You proved that all measures have nice properties. 5. You looked at the concepts of almost everywhere and complete measures. 6. We defined the notion of an A -measurable function. 7. We defined a simple A -measurable function. 8. We defined the integral of a non-negative simple A -measurable function. 9. We didn’t quite show that the definition was independent of our representation of the simple function.
Today 1. We will show that every non-negative measurable function is an increasing limit of simple functions. 2. We will define the integral of a non-negative measurable function. 3. We will look at properties of the integral. 4. Notably the Monotone Convergence Theorem.
Today 1. We will show that every non-negative measurable function is an increasing limit of simple functions. 2. We will define the integral of a non-negative measurable function. 3. We will look at properties of the integral. 4. Notably the Monotone Convergence Theorem.
Today 1. We will show that every non-negative measurable function is an increasing limit of simple functions. 2. We will define the integral of a non-negative measurable function. 3. We will look at properties of the integral. 4. Notably the Monotone Convergence Theorem.
Today 1. We will show that every non-negative measurable function is an increasing limit of simple functions. 2. We will define the integral of a non-negative measurable function. 3. We will look at properties of the integral. 4. Notably the Monotone Convergence Theorem.
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