Retrieve the values from a column based on earliest date column for each row it applies

Create this measure and put it visual level filter

Measure 3 = 
var __id = min(Sheet1[hostname])
var __date = CALCULATE(max(Sheet1[action_start]),ALLSELECTED(Sheet1),Sheet1[hostname]=__id)
return
CALCULATE(COUNT(Sheet1[action_id]),VALUES(Sheet1[hostname]),Sheet1[hostname]=__id , Sheet1[action_start]=__date)

Link : https://www.dropbox.com/s/bqd9vxp97cgm2u6/firstAction.pbix?dl=0

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Thanks. My Recent Blogs -Decoding Direct Query - Time Intelligence, Winner Coloring on MAP, HR Analytics, Power BI Working with Non-Standard TimeAnd Comparing Data Across Date Ranges
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