James Baxter
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Several definitions of Approximate continuity of real functions
2 votes

I will refer to the three definitions of approximate continuity given as AC0, AC1 and AC2 respectively and show they are all equivalent. AC1 iff AC2: Given a set $A$ by AC1, $A$ has density 1, $A$ is ...

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Concrete example of BV function $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative
0 votes

You could take $u$ to be the indicator function of a square. Then the jump part will be supported on the boundary of the square.

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Reference request: book on stochastic calculus (not finance)
3 votes

Le Gall's "Brownian Motion, Martingales and Stochastic Calculus" may be a good fit. You need to be comfortable with functional analysis though, cause he uses it sometimes to streamline proofs.

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