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Community Bot
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Let $d = 2$. Do we have that with $P_x$—probability $1$, for every $T> 0$ the complement $W[0, T]^c$ of the Brownian path up to time $T$ has infinitely many connected components?

I had seen this postpost, and I was wondering if this result is also covered in the 1954 Dvoretsky/Erdos/Kakutani paper. If not, can somebody provide me a reference/supply an answer?

Let $d = 2$. Do we have that with $P_x$—probability $1$, for every $T> 0$ the complement $W[0, T]^c$ of the Brownian path up to time $T$ has infinitely many connected components?

I had seen this post, and I was wondering if this result is also covered in the 1954 Dvoretsky/Erdos/Kakutani paper. If not, can somebody provide me a reference/supply an answer?

Let $d = 2$. Do we have that with $P_x$—probability $1$, for every $T> 0$ the complement $W[0, T]^c$ of the Brownian path up to time $T$ has infinitely many connected components?

I had seen this post, and I was wondering if this result is also covered in the 1954 Dvoretsky/Erdos/Kakutani paper. If not, can somebody provide me a reference/supply an answer?

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Edward Hoenn
Edward Hoenn
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In the plane, does complement of Brownian path have infinitely many connected components?

Let $d = 2$. Do we have that with $P_x$—probability $1$, for every $T> 0$ the complement $W[0, T]^c$ of the Brownian path up to time $T$ has infinitely many connected components?

I had seen this post, and I was wondering if this result is also covered in the 1954 Dvoretsky/Erdos/Kakutani paper. If not, can somebody provide me a reference/supply an answer?