Let N be a nonempty set and B a o-ring on N. Let µ, v be two measures on B and μ(A) < ν(Α), A € B. Show that fdµ < / fdv or all nonnegative measurable f :N→ [0, ∞0].

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let N be a nonempty set and B a o-ring on N.
Let µ, v be two measures on B and
H(A) < v(A),
А В.
Show that
for all nonnegative measurable f : N → [0, 0∞].
Transcribed Image Text:Let N be a nonempty set and B a o-ring on N. Let µ, v be two measures on B and H(A) < v(A), А В. Show that for all nonnegative measurable f : N → [0, 0∞].
Expert Solution
Step 1

Let Ω be a non- empty set.

And B a sigma ring on Ω.

Let μ,ν be the two measures on B

And ΩAνAAB.

The objective is to show that fdμfdν for all non-negative measurable f:Ω0,.

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