Ytukyg

2 Dear experienced community, I can't find an elegant solution to my problem. I have a subsample of my dataset which I want to resample weekly, but starting some weeks before the first entry in my data frame (so a few weeks with 0 counts) A sample of the data: In: print(df_pec.head()) Out: Count Image_Sequence_DateTime 18 1 2015-11-06 03:22:19 21 1 2015-11-11 01:48:51 22 1 2015-11-11 07:30:47 37 1 2015-11-25 09:42:23 48 1 2015-12-05 12:12:34 With the earliest image sequence at: In: df_pec.Image_Sequence_DateTime.min() Out: 2015-09-30 15:16:38 I have another function that gives me the starting point of the first week and the last point of the last week ever measured in that experiment, which are: In: print(s_startend) Out: ...

4 2 $begingroup$ In the book "Measure Theory" of Bogachev, vol. 2, Lemma 7.2.6 states the following. Let $mu$ be a $tau$ -additive, regular Borel measure on a topological space $X$ , and let ${f_alpha}$ be an increasing net of lower-semicontinuous non-negative functions such that $f:= lim_alpha f_alpha$ is bounded. Then $$ lim_alpha int_X f_alpha , dmu quad = quad int_X f , dmu . $$ In the proof it is quite clear where the $tau$ -additivity comes into play. However, I cannot see why we need $mu$ to be regular . Bogachev defines this property in the following way (paraphrasing its Definition 7.1.5): A measure $mu$ on a topological space $X$ is called regular if for every measurable set $Asubseteq X$ and for every $varepsilon > 0$ there exists a closed set $C_varepsilon subset...