My Apologies
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Transcript of My Apologies
My Apologies
Joint work with Gui-Qiang Chen, Monica Torres
The Problem
The answer is Yes – Main Result
When F is assumed to be only bounded, measurableWe can’t expect the same answer
What measures are admissible?
One of the Fundamental results of GMT
Sets of Finite Perimeter
The Density Topology
The Density Topology – The Union of uncountably many measurable sets Is still measurable
The measure-theoretic normal to an arbitrary measurable set
The Set E lies on one side of the plane determined by the normal
The Reduced Boundary of E
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A Pathological Example
More of Example – Swiss Cheese
Example of F in 3-space
Fuglede: The notion of “almost every set”
Ties to potential theory and Complex analysis
A Slight Diversion – The Coarea Formula
Fuglede’s result in a more meaningful setting
The Normal Trace of F on an arbitrary set
Preliminary result
More of the Hypothesis
Proof of the Result
Consider fields F that are bounded and for which the divergence is a signed measure
The Divergence Theorem for “almost every set” Fuglede
Proof of Fuglede’s Result – Quick Sketch
The Main Problem
Definition of Normal Trace