Using strong law of large numbers to construct a measure
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How can I apply the strong law of large numbers to construct a measure ${mu_p}$ on $([0,1],mathcal{B}([0,1]))$ such that ${mu_p}$'s are singular to $lambda_{Leb}$ and the distribution function of $mu_p$ is continuous?
To be more precise for such $mu_p$, if $p_1 neq p_2$, then $mu_{p_1} perp mu_{p_2}$, and in particular if $p neq frac{1}{2}$, $mu_p perp lambda$ where $lambda$ is the Lebesgue measure on $mathbb{R}$.
probability-theory lebesgue-measure law-of-large-numbers
asked Nov 15 at 16:48
Weak Nullstellensatz
163
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up vote
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How can I apply the strong law of large numbers to construct a measure ${mu_p}$ on $([0,1],mathcal{B}([0,1]))$ such that ${mu_p}$'s are singular to $lambda_{Leb}$ and the distribution function of $mu_p$ is continuous?
To be more precise for such $mu_p$, if $p_1 neq p_2$, then $mu_{p_1} perp mu_{p_2}$, and in particular if $p neq frac{1}{2}$, $mu_p perp lambda$ where $lambda$ is the Lebesgue measure on $mathbb{R}$.
probability-theory lebesgue-measure law-of-large-numbers
asked Nov 15 at 16:48
Weak Nullstellensatz
163
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How can I apply the strong law of large numbers to construct a measure ${mu_p}$ on $([0,1],mathcal{B}([0,1]))$ such that ${mu_p}$'s are singular to $lambda_{Leb}$ and the distribution function of $mu_p$ is continuous?
To be more precise for such $mu_p$, if $p_1 neq p_2$, then $mu_{p_1} perp mu_{p_2}$, and in particular if $p neq frac{1}{2}$, $mu_p perp lambda$ where $lambda$ is the Lebesgue measure on $mathbb{R}$.
probability-theory lebesgue-measure law-of-large-numbers
asked Nov 15 at 16:48
Weak Nullstellensatz
163
How can I apply the strong law of large numbers to construct a measure ${mu_p}$ on $([0,1],mathcal{B}([0,1]))$ such that ${mu_p}$'s are singular to $lambda_{Leb}$ and the distribution function of $mu_p$ is continuous?
To be more precise for such $mu_p$, if $p_1 neq p_2$, then $mu_{p_1} perp mu_{p_2}$, and in particular if $p neq frac{1}{2}$, $mu_p perp lambda$ where $lambda$ is the Lebesgue measure on $mathbb{R}$.
probability-theory lebesgue-measure law-of-large-numbers
probability-theory lebesgue-measure law-of-large-numbers
asked Nov 15 at 16:48
Weak Nullstellensatz
163
asked Nov 15 at 16:48
Weak Nullstellensatz
163
asked Nov 15 at 16:48
Weak Nullstellensatz
163
asked Nov 15 at 16:48
Weak Nullstellensatz
163
asked Nov 15 at 16:48
Weak Nullstellensatz
163
163
add a comment |
add a comment |
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